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'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fas", "fa-copy"); + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-times"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-times"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function() { + $('#documenter .docs-navbar').headroom({ + "tolerance": {"up": 10, "down": 10}, + }); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function() { + var settings = $('#documenter-settings'); + $('#documenter-settings-button').click(function(){ + settings.toggleClass('is-active'); + }); + // Close the dialog if X is clicked + $('#documenter-settings button.delete').click(function(){ + settings.removeClass('is-active'); + }); + // Close dialog if ESC is pressed + $(document).keyup(function(e) { + if (e.keyCode == 27) settings.removeClass('is-active'); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function() { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button") + sidebar_button.click(function(ev) { + ev.preventDefault(); + sidebar.toggleClass('visible'); + if (sidebar.hasClass('visible')) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind('click', function(ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + }); +}) + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function() { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css('max-width'), 10); + var L0 = e.width(); + if(L0 > L) { + var h0 = parseInt(e.css('font-size'), 10); + e.css('font-size', L * h0 / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on('orientationchange', resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function() { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if(typeof active !== 'undefined') { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +function set_theme(theme) { + var active = null; + var disabled = []; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + var themename = ss.ownerNode.getAttribute("data-theme-name"); + if(themename === null) continue; // ignore non-theme stylesheets + // Find the active theme + if(themename === theme) active = ss; + else disabled.push(ss); + } + if(active !== null) { + active.disabled = false; + if(active.ownerNode.getAttribute("data-theme-primary") === null) { + document.getElementsByTagName('html')[0].className = "theme--" + theme; + } else { + document.getElementsByTagName('html')[0].className = ""; + } + disabled.forEach(function(ss){ + ss.disabled = true; + }); + } + + // Store the theme in localStorage + if(typeof(window.localStorage) !== "undefined") { + window.localStorage.setItem("documenter-theme", theme); + } else { + console.error("Browser does not support window.localStorage"); + } +} + +// Theme picker setup +$(document).ready(function() { + // onchange callback + $('#documenter-themepicker').change(function themepick_callback(ev){ + var themename = $('#documenter-themepicker option:selected').attr('value'); + set_theme(themename); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if(typeof(window.localStorage) !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if(theme !== null) { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = (e.value === theme); + }) + } else { + $('#documenter-themepicker option').each(function(i,e) { + e.selected = $("html").hasClass(`theme--${e.value}`); + }) + } + } +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function() { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector 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+//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
  • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/previews/PR2081/assets/themes/documenter-dark.css b/previews/PR2081/assets/themes/documenter-dark.css new file 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content 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.button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-outlined.is-focused{background-color:#9e1b0d;border-color:#9e1b0d;color:#fff}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#9e1b0d;box-shadow:none;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#9e1b0d}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #9e1b0d #9e1b0d !important}html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:3px;font-size:.85em}html.theme--documenter-dark .button.is-normal{font-size:15px}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#dbdee0;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em / 2));top:calc(50% - (1em / 2));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:3px;font-size:.85em}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}html.theme--documenter-dark .container.is-fluid{margin-left:32px;margin-right:32px;max-width:none}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen{max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd{max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container{max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container{max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.85em}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--documenter-dark .icon.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--documenter-dark .icon.is-medium{height:2rem;width:2rem}html.theme--documenter-dark .icon.is-large{height:3rem;width:3rem}html.theme--documenter-dark .image,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--documenter-dark .image img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:290486px}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 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1055px){html.theme--documenter-dark .columns.is-variable.is-7-tablet-only{--columnGap: 1.75rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-7-touch{--columnGap: 1.75rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-7-desktop{--columnGap: 1.75rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-7-desktop-only{--columnGap: 1.75rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen{--columnGap: 1.75rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only{--columnGap: 1.75rem}}@media screen and (min-width: 1408px){html.theme--documenter-dark .columns.is-variable.is-7-fullhd{--columnGap: 1.75rem}}html.theme--documenter-dark .columns.is-variable.is-8{--columnGap: 2rem}@media screen and (max-width: 768px){html.theme--documenter-dark .columns.is-variable.is-8-mobile{--columnGap: 2rem}}@media screen and (min-width: 769px),print{html.theme--documenter-dark .columns.is-variable.is-8-tablet{--columnGap: 2rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-8-tablet-only{--columnGap: 2rem}}@media screen and (max-width: 1055px){html.theme--documenter-dark .columns.is-variable.is-8-touch{--columnGap: 2rem}}@media screen and (min-width: 1056px){html.theme--documenter-dark .columns.is-variable.is-8-desktop{--columnGap: 2rem}}@media screen and (min-width: 1056px) and (max-width: 1215px){html.theme--documenter-dark .columns.is-variable.is-8-desktop-only{--columnGap: 2rem}}@media screen and (min-width: 1216px){html.theme--documenter-dark .columns.is-variable.is-8-widescreen{--columnGap: 2rem}}@media screen and (min-width: 1216px) and (max-width: 1407px){html.theme--documenter-dark 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span.sgr102{background-color:#0e8300}.ansi span.sgr103{background-color:#a98800}.ansi span.sgr104{background-color:#3c5dcd}.ansi span.sgr105{background-color:#9256af}.ansi span.sgr106{background-color:#008fa3}.ansi span.sgr107{background-color:#f5f5f5}code.language-julia-repl>span.hljs-meta{color:#066f00;font-weight:bolder}/*! + Theme: Default + Description: Original highlight.js style + Author: (c) Ivan Sagalaev + Maintainer: @highlightjs/core-team + Website: https://highlightjs.org/ + License: see project LICENSE + Touched: 2021 +*/pre code.hljs{display:block;overflow-x:auto}code.hljs{padding:3px 5px}.hljs{background:#F0F0F0;color:#444}.hljs-comment{color:#888888}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta 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    Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/previews/PR2081/dae/fully_implicit/index.html b/previews/PR2081/dae/fully_implicit/index.html new file mode 100644 index 0000000000..928295b7d9 --- /dev/null +++ b/previews/PR2081/dae/fully_implicit/index.html @@ -0,0 +1,6 @@ + +Methods for Fully Implicit ODEs (DAEProblem) · OrdinaryDiffEq.jl
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    Methods for Fully Implicit ODEs (DAEProblem)

    Missing docstring.

    Missing docstring for DImplicitEuler. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for DABDF2. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for DFBDF. Check Documenter's build log for details.

    diff --git a/previews/PR2081/dynamical/nystrom/index.html b/previews/PR2081/dynamical/nystrom/index.html new file mode 100644 index 0000000000..4abc7261b5 --- /dev/null +++ b/previews/PR2081/dynamical/nystrom/index.html @@ -0,0 +1,24 @@ + +Runge-Kutta Nystrom Methods · OrdinaryDiffEq.jl
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    Runge-Kutta Nystrom Methods

    OrdinaryDiffEq.IRKN3 — Type
    IRKN3

    Improved Runge-Kutta-Nyström method of order three, which minimizes the amount of evaluated functions in each step. Fixed time steps only.

    Second order ODE should not depend on the first derivative.

    References

    @article{rabiei2012numerical, title={Numerical Solution of Second-Order Ordinary Differential Equations by Improved Runge-Kutta Nystrom Method}, author={Rabiei, Faranak and Ismail, Fudziah and Norazak, S and Emadi, Saeid}, publisher={Citeseer} }

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    OrdinaryDiffEq.IRKN4 — Type
    IRKN4

    Improves Runge-Kutta-Nyström method of order four, which minimizes the amount of evaluated functions in each step. Fixed time steps only.

    Second order ODE should not be dependent on the first derivative.

    Recommended for smooth problems with expensive functions to evaluate.

    References

    @article{rabiei2012numerical, title={Numerical Solution of Second-Order Ordinary Differential Equations by Improved Runge-Kutta Nystrom Method}, author={Rabiei, Faranak and Ismail, Fudziah and Norazak, S and Emadi, Saeid}, publisher={Citeseer} }

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    OrdinaryDiffEq.Nystrom4 — Type
    Nystrom4

    A 4th order explicit Runge-Kutta-Nyström method which can be applied directly on second order ODEs. Can only be used with fixed time steps.

    In case the ODE Problem is not dependent on the first derivative consider using Nystrom4VelocityIndependent to increase performance.

    References

    E. Hairer, S.P. Norsett, G. Wanner, (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series in Computational Mathematics, Springer-Verlag.

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    OrdinaryDiffEq.Nystrom4VelocityIndependent — Type
    Nystrom4VelocityIdependent

    A 4th order explicit Runkge-Kutta-Nyström method. Used directly on second order ODEs, where the acceleration is independent from velocity (ODE Problem is not dependent on the first derivative).

    More efficient then Nystrom4 on velocity independent problems, since less evaluations are needed.

    Fixed time steps only.

    References

    E. Hairer, S.P. Norsett, G. Wanner, (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series in Computational Mathematics, Springer-Verlag.

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    OrdinaryDiffEq.Nystrom5VelocityIndependent — Type
    Nystrom5VelocityIndependent

    A 5th order explicit Runkge-Kutta-Nyström method. Used directly on second order ODEs, where the acceleration is independent from velocity (ODE Problem is not dependent on the first derivative). Fixed time steps only.

    References

    E. Hairer, S.P. Norsett, G. Wanner, (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series in Computational Mathematics, Springer-Verlag.

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    OrdinaryDiffEq.FineRKN4 — Type
    FineRKN4()

    A 4th order explicit Runge-Kutta-Nyström method which can be applied directly to second order ODEs. In particular, this method allows the acceleration equation to depend on the velocity.

    References

    @article{fine1987low,
+  title={Low order practical {R}unge-{K}utta-{N}ystr{"o}m methods},
+  author={Fine, Jerry Michael},
+  journal={Computing},
+  volume={38},
+  number={4},
+  pages={281--297},
+  year={1987},
+  publisher={Springer}
+}
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    OrdinaryDiffEq.FineRKN5 — Type
    FineRKN5()

    A 5th order explicit Runge-Kutta-Nyström method which can be applied directly to second order ODEs. In particular, this method allows the acceleration equation to depend on the velocity.

    References

    @article{fine1987low,
+  title={Low order practical {R}unge-{K}utta-{N}ystr{"o}m methods},
+  author={Fine, Jerry Michael},
+  journal={Computing},
+  volume={38},
+  number={4},
+  pages={281--297},
+  year={1987},
+  publisher={Springer}
+}
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    OrdinaryDiffEq.DPRKN6 — Type
    DPRKN6

    6th order explicit Runge-Kutta-Nyström method. The second order ODE should not depend on the first derivative. Free 6th order interpolant.

    References

    @article{dormand1987runge, title={Runge-kutta-nystrom triples}, author={Dormand, JR and Prince, PJ}, journal={Computers \& Mathematics with Applications}, volume={13}, number={12}, pages={937–949}, year={1987}, publisher={Elsevier} }

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    OrdinaryDiffEq.DPRKN6FM — Type
    DPRKN6FM

    6th order explicit Runge-Kutta-Nyström method. The second order ODE should not depend on the first derivative.

    Compared to DPRKN6, this method has smaller truncation error coefficients which leads to performance gain when only the main solution points are considered.

    References

    @article{Dormand1987FamiliesOR, title={Families of Runge-Kutta-Nystrom Formulae}, author={J. R. Dormand and Moawwad E. A. El-Mikkawy and P. J. Prince}, journal={Ima Journal of Numerical Analysis}, year={1987}, volume={7}, pages={235-250} }

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    OrdinaryDiffEq.DPRKN8 — Type
    DPRKN8

    8th order explicit Runge-Kutta-Nyström method. The second order ODE should not depend on the first derivative.

    Not as efficient as DPRKN12 when high accuracy is needed, however this solver is competitive with DPRKN6 at lax tolerances and, depending on the problem, might be a good option between performance and accuracy.

    References

    @article{dormand1987high, title={High-order embedded Runge-Kutta-Nystrom formulae}, author={Dormand, JR and El-Mikkawy, MEA and Prince, PJ}, journal={IMA Journal of Numerical Analysis}, volume={7}, number={4}, pages={423–430}, year={1987}, publisher={Oxford University Press} }

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    OrdinaryDiffEq.DPRKN12 — Type
    DPRKN12

    12th order explicit Rugne-Kutta-Nyström method. The second order ODE should not depend on the first derivative.

    Most efficient when high accuracy is needed.

    References

    @article{dormand1987high, title={High-order embedded Runge-Kutta-Nystrom formulae}, author={Dormand, JR and El-Mikkawy, MEA and Prince, PJ}, journal={IMA Journal of Numerical Analysis}, volume={7}, number={4}, pages={423–430}, year={1987}, publisher={Oxford University Press} }

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    OrdinaryDiffEq.ERKN4 — Type
    ERKN4

    Embedded 4(3) pair of explicit Runge-Kutta-Nyström methods. Integrates the periodic properties of the harmonic oscillator exactly.

    The second order ODE should not depend on the first derivative.

    Uses adaptive step size control. This method is extra efficient on periodic problems.

    References

    @article{demba2017embedded, title={An Embedded 4 (3) Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nystr{"o}m Method for Solving Periodic Initial Value Problems}, author={Demba, MA and Senu, N and Ismail, F}, journal={Applied Mathematical Sciences}, volume={11}, number={17}, pages={819–838}, year={2017} }

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    OrdinaryDiffEq.ERKN5 — Type
    ERKN5

    Embedded 5(4) pair of explicit Runge-Kutta-Nyström methods. Integrates the periodic properties of the harmonic oscillator exactly.

    The second order ODE should not depend on the first derivative.

    Uses adaptive step size control. This method is extra efficient on periodic problems.

    References

    @article{demba20165, title={A 5 (4) Embedded Pair of Explicit Trigonometrically-Fitted Runge–Kutta–Nystr{"o}m Methods for the Numerical Solution of Oscillatory Initial Value Problems}, author={Demba, Musa A and Senu, Norazak and Ismail, Fudziah}, journal={Mathematical and Computational Applications}, volume={21}, number={4}, pages={46}, year={2016}, publisher={Multidisciplinary Digital Publishing Institute} }

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    OrdinaryDiffEq.ERKN7 — Type
    ERKN7

    Embedded pair of explicit Runge-Kutta-Nyström methods. Integrates the periodic properties of the harmonic oscillator exactly.

    The second order ODE should not depend on the first derivative.

    Uses adaptive step size control. This method is extra efficient on periodic Problems.

    References

    @article{SimosOnHO, title={On high order Runge-Kutta-Nystr{"o}m pairs}, author={Theodore E. Simos and Ch. Tsitouras}, journal={J. Comput. Appl. Math.}, volume={400}, pages={113753} }

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    diff --git a/previews/PR2081/dynamical/symplectic/index.html b/previews/PR2081/dynamical/symplectic/index.html new file mode 100644 index 0000000000..c95fea9388 --- /dev/null +++ b/previews/PR2081/dynamical/symplectic/index.html @@ -0,0 +1,6 @@ + +Symplectic Runge-Kutta Methods · OrdinaryDiffEq.jl
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    Symplectic Runge-Kutta Methods

    Missing docstring.

    Missing docstring for SymplecticEuler. Check Documenter's build log for details.

    OrdinaryDiffEq.VelocityVerlet — Type

    @article{verlet1967computer, title={Computer" experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules}, author={Verlet, Loup}, journal={Physical review}, volume={159}, number={1}, pages={98}, year={1967}, publisher={APS} }

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    OrdinaryDiffEq.VerletLeapfrog — Type

    @article{verlet1967computer, title={Computer" experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules}, author={Verlet, Loup}, journal={Physical review}, volume={159}, number={1}, pages={98}, year={1967}, publisher={APS} }

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    OrdinaryDiffEq.PseudoVerletLeapfrog — Type

    @article{verlet1967computer, title={Computer" experiments" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules}, author={Verlet, Loup}, journal={Physical review}, volume={159}, number={1}, pages={98}, year={1967}, publisher={APS} }

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    OrdinaryDiffEq.McAte2 — Type

    @article{mclachlan1992accuracy, title={The accuracy of symplectic integrators}, author={McLachlan, Robert I and Atela, Pau}, journal={Nonlinearity}, volume={5}, number={2}, pages={541}, year={1992}, publisher={IOP Publishing} }

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    OrdinaryDiffEq.Ruth3 — Type

    @article{ruth1983canonical, title={A canonical integration technique}, author={Ruth, Ronald D}, journal={IEEE Trans. Nucl. Sci.}, volume={30}, number={CERN-LEP-TH-83-14}, pages={2669–2671}, year={1983} }

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    OrdinaryDiffEq.McAte3 — Type

    @article{mclachlan1992accuracy, title={The accuracy of symplectic integrators}, author={McLachlan, Robert I and Atela, Pau}, journal={Nonlinearity}, volume={5}, number={2}, pages={541}, year={1992}, publisher={IOP Publishing} }

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    OrdinaryDiffEq.CandyRoz4 — Type

    @article{candy1991symplectic, title={A symplectic integration algorithm for separable Hamiltonian functions}, author={Candy, J and Rozmus, W}, journal={Journal of Computational Physics}, volume={92}, number={1}, pages={230–256}, year={1991}, publisher={Elsevier} }

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    Missing docstring.

    Missing docstring for McAte4. Check Documenter's build log for details.

    OrdinaryDiffEq.CalvoSanz4 — Type

    @article{sanz1993symplectic, title={Symplectic numerical methods for Hamiltonian problems}, author={Sanz-Serna, Jes{'u}s Maria and Calvo, Mari-Paz}, journal={International Journal of Modern Physics C}, volume={4}, number={02}, pages={385–392}, year={1993}, publisher={World Scientific} }

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    OrdinaryDiffEq.McAte42 — Type

    @article{mclachlan1992accuracy, title={The accuracy of symplectic integrators}, author={McLachlan, Robert I and Atela, Pau}, journal={Nonlinearity}, volume={5}, number={2}, pages={541}, year={1992}, publisher={IOP Publishing} }

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    OrdinaryDiffEq.McAte5 — Type

    @article{mclachlan1992accuracy, title={The accuracy of symplectic integrators}, author={McLachlan, Robert I and Atela, Pau}, journal={Nonlinearity}, volume={5}, number={2}, pages={541}, year={1992}, publisher={IOP Publishing} }

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    OrdinaryDiffEq.Yoshida6 — Type

    @article{yoshida1990construction, title={Construction of higher order symplectic integrators}, author={Yoshida, Haruo}, journal={Physics letters A}, volume={150}, number={5-7}, pages={262–268}, year={1990}, publisher={Elsevier} }

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    OrdinaryDiffEq.KahanLi6 — Type

    @article{kahan1997composition, title={Composition constants for raising the orders of unconventional schemes for ordinary differential equations}, author={Kahan, William and Li, Ren-Cang}, journal={Mathematics of computation}, volume={66}, number={219}, pages={1089–1099}, year={1997} }

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    OrdinaryDiffEq.McAte8 — Type

    @article{mclachlan1995numerical, title={On the numerical integration of ordinary differential equations by symmetric composition methods}, author={McLachlan, Robert I}, journal={SIAM Journal on Scientific Computing}, volume={16}, number={1}, pages={151–168}, year={1995}, publisher={SIAM} }

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    OrdinaryDiffEq.KahanLi8 — Type

    @article{kahan1997composition, title={Composition constants for raising the orders of unconventional schemes for ordinary differential equations}, author={Kahan, William and Li, Ren-Cang}, journal={Mathematics of computation}, volume={66}, number={219}, pages={1089–1099}, year={1997} }

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    OrdinaryDiffEq.SofSpa10 — Type

    @article{sofroniou2005derivation, title={Derivation of symmetric composition constants for symmetric integrators}, author={Sofroniou, Mark and Spaletta, Giulia}, journal={Optimization Methods and Software}, volume={20}, number={4-5}, pages={597–613}, year={2005}, publisher={Taylor \& Francis} }

    source
    diff --git a/previews/PR2081/imex/imex_multistep/index.html b/previews/PR2081/imex/imex_multistep/index.html new file mode 100644 index 0000000000..5ae28f3bd3 --- /dev/null +++ b/previews/PR2081/imex/imex_multistep/index.html @@ -0,0 +1,6 @@ + +IMEX Multistep Methods · OrdinaryDiffEq.jl
    Edit on GitHub

    IMEX Multistep Methods

    Missing docstring.

    Missing docstring for CNAB2. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for CNLF2. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for SBDF. Check Documenter's build log for details.

    OrdinaryDiffEq.SBDF2 — Function
    SBDF2(;kwargs...)

    The two-step version of the IMEX multistep methods of

    • Uri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037

    See also SBDF.

    source
    OrdinaryDiffEq.SBDF3 — Function
    SBDF3(;kwargs...)

    The three-step version of the IMEX multistep methods of

    • Uri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037

    See also SBDF.

    source
    OrdinaryDiffEq.SBDF4 — Function
    SBDF4(;kwargs...)

    The four-step version of the IMEX multistep methods of

    • Uri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037

    See also SBDF.

    source
    diff --git a/previews/PR2081/imex/imex_sdirk/index.html b/previews/PR2081/imex/imex_sdirk/index.html new file mode 100644 index 0000000000..210e34c561 --- /dev/null +++ b/previews/PR2081/imex/imex_sdirk/index.html @@ -0,0 +1,7 @@ + +IMEX SDIRK Methods · OrdinaryDiffEq.jl
    Edit on GitHub

    IMEX SDIRK Methods

    OrdinaryDiffEq.IMEXEuler — Function
    IMEXEuler(;kwargs...)

    The one-step version of the IMEX multistep methods of

    • Uri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037

    When applied to a SplitODEProblem of the form

    u'(t) = f1(u) + f2(u)

    The default IMEXEuler() method uses an update of the form

    unew = uold + dt * (f1(unew) + f2(uold))

    See also SBDF, IMEXEulerARK.

    source
    OrdinaryDiffEq.IMEXEulerARK — Function
    IMEXEulerARK(;kwargs...)

    The one-step version of the IMEX multistep methods of

    • Uri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037

    When applied to a SplitODEProblem of the form

    u'(t) = f1(u) + f2(u)

    A classical additive Runge-Kutta method in the sense of Araújo, Murua, Sanz-Serna (1997) consisting of the implicit and the explicit Euler method given by

    y1   = uold + dt * f1(y1)
+unew = uold + dt * (f1(unew) + f2(y1))

    See also SBDF, IMEXEuler.

    source
    OrdinaryDiffEq.KenCarp3 — Type

    @book{kennedy2001additive, title={Additive Runge-Kutta schemes for convection-diffusion-reaction equations}, author={Kennedy, Christopher Alan}, year={2001}, publisher={National Aeronautics and Space Administration, Langley Research Center} }

    KenCarp3: SDIRK Method An A-L stable stiffly-accurate 3rd order ESDIRK method with splitting

    source
    OrdinaryDiffEq.KenCarp4 — Type

    @book{kennedy2001additive, title={Additive Runge-Kutta schemes for convection-diffusion-reaction equations}, author={Kennedy, Christopher Alan}, year={2001}, publisher={National Aeronautics and Space Administration, Langley Research Center} }

    KenCarp4: SDIRK Method An A-L stable stiffly-accurate 4th order ESDIRK method with splitting

    source
    OrdinaryDiffEq.KenCarp47 — Type

    @article{kennedy2019higher, title={Higher-order additive Runge–Kutta schemes for ordinary differential equations}, author={Kennedy, Christopher A and Carpenter, Mark H}, journal={Applied Numerical Mathematics}, volume={136}, pages={183–205}, year={2019}, publisher={Elsevier} }

    KenCarp47: SDIRK Method An A-L stable stiffly-accurate 4th order seven-stage ESDIRK method with splitting

    source
    OrdinaryDiffEq.KenCarp5 — Type

    @book{kennedy2001additive, title={Additive Runge-Kutta schemes for convection-diffusion-reaction equations}, author={Kennedy, Christopher Alan}, year={2001}, publisher={National Aeronautics and Space Administration, Langley Research Center} }

    KenCarp5: SDIRK Method An A-L stable stiffly-accurate 5th order ESDIRK method with splitting

    source
    OrdinaryDiffEq.KenCarp58 — Type

    @article{kennedy2019higher, title={Higher-order additive Runge–Kutta schemes for ordinary differential equations}, author={Kennedy, Christopher A and Carpenter, Mark H}, journal={Applied Numerical Mathematics}, volume={136}, pages={183–205}, year={2019}, publisher={Elsevier} }

    KenCarp58: SDIRK Method An A-L stable stiffly-accurate 5th order eight-stage ESDIRK method with splitting

    source
    Missing docstring.

    Missing docstring for ESDIRK54I8L2SA. Check Documenter's build log for details.

    OrdinaryDiffEq.ESDIRK436L2SA2 — Type

    @article{Kennedy2019DiagonallyIR, title={Diagonally implicit Runge–Kutta methods for stiff ODEs}, author={Christopher A. Kennedy and Mark H. Carpenter}, journal={Applied Numerical Mathematics}, year={2019}, volume={146}, pages={221-244} }

    source
    OrdinaryDiffEq.ESDIRK437L2SA — Type

    @article{Kennedy2019DiagonallyIR, title={Diagonally implicit Runge–Kutta methods for stiff ODEs}, author={Christopher A. Kennedy and Mark H. Carpenter}, journal={Applied Numerical Mathematics}, year={2019}, volume={146}, pages={221-244} }

    source
    OrdinaryDiffEq.ESDIRK547L2SA2 — Type

    @article{Kennedy2019DiagonallyIR, title={Diagonally implicit Runge–Kutta methods for stiff ODEs}, author={Christopher A. Kennedy and Mark H. Carpenter}, journal={Applied Numerical Mathematics}, year={2019}, volume={146}, pages={221-244} }

    source
    OrdinaryDiffEq.ESDIRK659L2SA — Type

    @article{Kennedy2019DiagonallyIR, title={Diagonally implicit Runge–Kutta methods for stiff ODEs}, author={Christopher A. Kennedy and Mark H. Carpenter}, journal={Applied Numerical Mathematics}, year={2019}, volume={146}, pages={221-244}

    Currently has STABILITY ISSUES, causing it to fail the adaptive tests. Check issue https://github.com/SciML/OrdinaryDiffEq.jl/issues/1933 for more details. }

    source
    diff --git a/previews/PR2081/index.html b/previews/PR2081/index.html new file mode 100644 index 0000000000..18b60e254d --- /dev/null +++ b/previews/PR2081/index.html @@ -0,0 +1,190 @@ + +OrdinaryDiffEq.jl: ODE solvers and utilities · OrdinaryDiffEq.jl
    Edit on GitHub

    OrdinaryDiffEq.jl

    OrdinaryDiffEq.jl is a component package in the DifferentialEquations ecosystem. It holds the ordinary differential equation solvers and utilities. While completely independent and usable on its own, users interested in using this functionality should check out DifferentialEquations.jl.

    Installation

    Assuming that you already have Julia correctly installed, it suffices to import OrdinaryDiffEq.jl in the standard way:

    import Pkg; Pkg.add("OrdinaryDiffEq")

    Reproducibility

    The documentation of this SciML package was built using these direct dependencies,
    Status `~/work/OrdinaryDiffEq.jl/OrdinaryDiffEq.jl/docs/Project.toml`
+⌅ [e30172f5] Documenter v0.27.25
+  [1dea7af3] OrdinaryDiffEq v6.61.0 `~/work/OrdinaryDiffEq.jl/OrdinaryDiffEq.jl`
+Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated`
    and using this machine and Julia version.
    Julia Version 1.9.4
+Commit 8e5136fa297 (2023-11-14 08:46 UTC)
+Build Info:
+  Official https://julialang.org/ release
+Platform Info:
+  OS: Linux (x86_64-linux-gnu)
+  CPU: 4 × AMD EPYC 7763 64-Core Processor
+  WORD_SIZE: 64
+  LIBM: libopenlibm
+  LLVM: libLLVM-14.0.6 (ORCJIT, znver3)
+  Threads: 1 on 4 virtual cores
    A more complete overview of all dependencies and their versions is also provided.
    Status `~/work/OrdinaryDiffEq.jl/OrdinaryDiffEq.jl/docs/Manifest.toml`
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+⌅ [e30172f5] Documenter v0.27.25
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+  [bb5d69b7] MaybeInplace v0.1.1
+  [e1d29d7a] Missings v1.1.0
+  [46d2c3a1] MuladdMacro v0.2.4
+  [d41bc354] NLSolversBase v7.8.3
+  [77ba4419] NaNMath v1.0.2
+  [8913a72c] NonlinearSolve v3.0.1
+  [6fe1bfb0] OffsetArrays v1.12.10
+  [bac558e1] OrderedCollections v1.6.3
+  [1dea7af3] OrdinaryDiffEq v6.61.0 `~/work/OrdinaryDiffEq.jl/OrdinaryDiffEq.jl`
+  [65ce6f38] PackageExtensionCompat v1.0.2
+  [d96e819e] Parameters v0.12.3
+  [69de0a69] Parsers v2.8.0
+  [f517fe37] Polyester v0.7.9
+  [1d0040c9] PolyesterWeave v0.2.1
+  [d236fae5] PreallocationTools v0.4.12
+  [aea7be01] PrecompileTools v1.2.0
+  [21216c6a] Preferences v1.4.1
+  [27ebfcd6] Primes v0.5.5
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+  [3f19e933] p7zip_jll v17.4.0+0
+Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`
    You can also download the +manifest file and the +project file.
    diff --git a/previews/PR2081/misc/index.html b/previews/PR2081/misc/index.html new file mode 100644 index 0000000000..ad3feb585d --- /dev/null +++ b/previews/PR2081/misc/index.html @@ -0,0 +1,6 @@ + +- · OrdinaryDiffEq.jl
    Edit on GitHub
    Missing docstring.

    Missing docstring for LinearExponential. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for SplitEuler. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for CompositeAlgorithm. Check Documenter's build log for details.

    OrdinaryDiffEq.PDIRK44 — Type

    PDIRK44: Parallel Diagonally Implicit Runge-Kutta Method A 2 processor 4th order diagonally non-adaptive implicit method.

    source
    diff --git a/previews/PR2081/nonstiff/explicit_extrapolation/index.html b/previews/PR2081/nonstiff/explicit_extrapolation/index.html new file mode 100644 index 0000000000..fa9353dff6 --- /dev/null +++ b/previews/PR2081/nonstiff/explicit_extrapolation/index.html @@ -0,0 +1,6 @@ + +Explicit Extrapolation Methods · OrdinaryDiffEq.jl
    Edit on GitHub

    Explicit Extrapolation Methods

    diff --git a/previews/PR2081/nonstiff/explicitrk/index.html b/previews/PR2081/nonstiff/explicitrk/index.html new file mode 100644 index 0000000000..fb7e31bbc4 --- /dev/null +++ b/previews/PR2081/nonstiff/explicitrk/index.html @@ -0,0 +1,79 @@ + +Explicit Runge-Kutta Methods · OrdinaryDiffEq.jl
    Edit on GitHub

    Explicit Runge-Kutta Methods

    With the help of FastBroadcast.jl, we can use threaded parallelism to reduce compute time for all of the explicit Runge-Kutta methods! The thread option determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads. When we call solve(prob, alg(thread=OrdinaryDiffEq.True())), we can turn on the multithreading option to achieve acceleration (for sufficiently large problems).

    Standard Explicit Runge-Kutta Methods

    OrdinaryDiffEq.Heun — Type
    Heun(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. The second order Heun's method. Uses embedded Euler method for adaptivity.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.Ralston — Type
    Ralston(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. The optimized second order midpoint method. Uses embedded Euler method for adaptivity.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.Midpoint — Type
    Midpoint(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. The second order midpoint method. Uses embedded Euler method for adaptivity.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.RK4 — Type
    RK4(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. The canonical Runge-Kutta Order 4 method. Uses a defect control for adaptive stepping using maximum error over the whole interval.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    @article{shampine2005solving, title={Solving ODEs and DDEs with residual control}, author={Shampine, LF}, journal={Applied Numerical Mathematics}, volume={52}, number={1}, pages={113–127}, year={2005}, publisher={Elsevier} }

    source
    OrdinaryDiffEq.RKM — Type
    RKM(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. TBD

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.MSRK5 — Type
    MSRK5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. 5th order Explicit RK method.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Misha Stepanov - https://arxiv.org/pdf/2202.08443.pdf : Figure 3.

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    OrdinaryDiffEq.MSRK6 — Type
    MSRK6(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. 6th order Explicit RK method.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Misha Stepanov - https://arxiv.org/pdf/2202.08443.pdf : Table4

    source
    OrdinaryDiffEq.Anas5 — Type
    Anas5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        w = 1)

    Explicit Runge-Kutta Method. 4th order Runge-Kutta method designed for periodic problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • w: a periodicity estimate, which when accurate the method becomes 5th order (and is otherwise 4th order with less error for better estimates).

    References

    source
    OrdinaryDiffEq.RKO65 — Type
    RKO5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. 5th order Explicit RK method.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Tsitouras, Ch. "Explicit Runge–Kutta methods for starting integration of Lane–Emden problem." Applied Mathematics and Computation 354 (2019): 353-364. doi: https://doi.org/10.1016/j.amc.2019.02.047

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    OrdinaryDiffEq.OwrenZen3 — Type
    OwrenZen3(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Owren-Zennaro optimized interpolation 3/2 method (free 3rd order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    @article{owren1992derivation, title={Derivation of efficient, continuous, explicit Runge–Kutta methods}, author={Owren, Brynjulf and Zennaro, Marino}, journal={SIAM journal on scientific and statistical computing}, volume={13}, number={6}, pages={1488–1501}, year={1992}, publisher={SIAM} }

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    OrdinaryDiffEq.OwrenZen4 — Type
    OwrenZen4(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Owren-Zennaro optimized interpolation 4/3 method (free 4th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    @article{owren1992derivation, title={Derivation of efficient, continuous, explicit Runge–Kutta methods}, author={Owren, Brynjulf and Zennaro, Marino}, journal={SIAM journal on scientific and statistical computing}, volume={13}, number={6}, pages={1488–1501}, year={1992}, publisher={SIAM} }

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    OrdinaryDiffEq.OwrenZen5 — Type
    OwrenZen5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Owren-Zennaro optimized interpolation 5/4 method (free 5th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    @article{owren1992derivation, title={Derivation of efficient, continuous, explicit Runge–Kutta methods}, author={Owren, Brynjulf and Zennaro, Marino}, journal={SIAM journal on scientific and statistical computing}, volume={13}, number={6}, pages={1488–1501}, year={1992}, publisher={SIAM} }

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    OrdinaryDiffEq.BS3 — Type
    BS3(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, four-stage explicit FSAL Runge-Kutta method with embedded error estimator of Bogacki and Shampine.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    @article{bogacki19893, title={A 3 (2) pair of Runge-Kutta formulas}, author={Bogacki, Przemyslaw and Shampine, Lawrence F}, journal={Applied Mathematics Letters}, volume={2}, number={4}, pages={321–325}, year={1989}, publisher={Elsevier} }

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    OrdinaryDiffEq.DP5 — Type
    DP5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Dormand-Prince's 5/4 Runge-Kutta method. (free 4th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    @article{dormand1980family, title={A family of embedded Runge-Kutta formulae}, author={Dormand, John R and Prince, Peter J}, journal={Journal of computational and applied mathematics}, volume={6}, number={1}, pages={19–26}, year={1980}, publisher={Elsevier} }

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    OrdinaryDiffEq.Tsit5 — Type
    Tsit5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A fifth-order explicit Runge-Kutta method with embedded error estimator of Tsitouras. Free 4th order interpolant.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    @article{tsitouras2011runge, title={Runge–Kutta pairs of order 5 (4) satisfying only the first column simplifying assumption}, author={Tsitouras, Ch}, journal={Computers \& Mathematics with Applications}, volume={62}, number={2}, pages={770–775}, year={2011}, publisher={Elsevier} }

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    OrdinaryDiffEq.DP8 — Type
    DP8(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Hairer's 8/5/3 adaption of the Dormand-Prince Runge-Kutta method. (7th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    E. Hairer, S.P. Norsett, G. Wanner, (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series in Computational Mathematics, Springer-Verlag.

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    OrdinaryDiffEq.TanYam7 — Type
    TanYam7(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Tanaka-Yamashita 7 Runge-Kutta method. (7th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Tanaka M., Muramatsu S., Yamashita S., (1992), On the Optimization of Some Nine-Stage Seventh-order Runge-Kutta Method, Information Processing Society of Japan, 33 (12), pp. 1512-1526.

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    OrdinaryDiffEq.TsitPap8 — Type
    TsitPap8(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Tsitouras-Papakostas 8/7 Runge-Kutta method.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.Feagin10 — Type

    @article{feagin2012high, title={High-order explicit Runge-Kutta methods using m-symmetry}, author={Feagin, Terry}, year={2012}, publisher={Neural, Parallel \& Scientific Computations} }

    Feagin10: Explicit Runge-Kutta Method Feagin's 10th-order Runge-Kutta method.

    source
    OrdinaryDiffEq.Feagin12 — Type

    @article{feagin2012high, title={High-order explicit Runge-Kutta methods using m-symmetry}, author={Feagin, Terry}, year={2012}, publisher={Neural, Parallel \& Scientific Computations} }

    Feagin12: Explicit Runge-Kutta Method Feagin's 12th-order Runge-Kutta method.

    source
    OrdinaryDiffEq.Feagin14 — Type

    Feagin, T., “An Explicit Runge-Kutta Method of Order Fourteen,” Numerical Algorithms, 2009

    Feagin14: Explicit Runge-Kutta Method Feagin's 14th-order Runge-Kutta method.

    source
    OrdinaryDiffEq.FRK65 — Type
    FRK65(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        omega = 0.0)

    Explicit Runge-Kutta Method. Zero Dissipation Runge-Kutta of 6th order.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • omega: a periodicity phase estimate, when accurate this method results in zero numerical dissipation.

    References

    source
    OrdinaryDiffEq.PFRK87 — Type
    PFRK87(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        omega = 0.0)

    Explicit Runge-Kutta Method. Phase-fitted Runge-Kutta of 8th order.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • omega: a periodicity phase estimate, when accurate this method results in zero numerical dissipation.

    References

    source
    OrdinaryDiffEq.Stepanov5 — Type
    Stepanov5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. 5th order Explicit RK method.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    @article{Stepanov2021Embedded5, title={Embedded (4, 5) pairs of explicit 7-stage Runge–Kutta methods with FSAL property}, author={Misha Stepanov}, journal={Calcolo}, year={2021}, volume={59} }

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    OrdinaryDiffEq.SIR54 — Type
    SIR54(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+         step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+         thread = OrdinaryDiffEq.False())

    5th order Explicit RK method suited for SIR-type epidemic models.

    Like SSPRK methods, this method also takes optional arguments stage_limiter! and step_limiter!, where stage_limiter! and step_limiter! are functions of the form limiter!(u, integrator, p, t).

    The argument thread determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    Reference

    @article{Kovalnogov2020RungeKuttaPS, title={Runge–Kutta pairs suited for SIR‐type epidemic models}, author={Vladislav N. Kovalnogov and Theodore E. Simos and Ch. Tsitouras}, journal={Mathematical Methods in the Applied Sciences}, year={2020}, volume={44}, pages={5210 - 5216} }

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    OrdinaryDiffEq.Alshina2 — Type
    Alshina2(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+         step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+         thread = OrdinaryDiffEq.False())

    2nd order, 2-stage Explicit Runge-Kutta Method with optimal parameters.

    Like SSPRK methods, this method also takes optional arguments stage_limiter! and step_limiter!, where stage_limiter! and step_limiter! are functions of the form limiter!(u, integrator, p, t).

    The argument thread determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    Reference

    @article{Alshina2008, doi = {10.1134/s0965542508030068}, url = {https://doi.org/10.1134/s0965542508030068}, year = {2008}, month = mar, publisher = {Pleiades Publishing Ltd}, volume = {48}, number = {3}, pages = {395–405}, author = {E. A. Alshina and E. M. Zaks and N. N. Kalitkin}, title = {Optimal first- to sixth-order accurate Runge-Kutta schemes}, journal = {Computational Mathematics and Mathematical Physics} }

    source
    OrdinaryDiffEq.Alshina3 — Type
    Alshina3(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+         step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+         thread = OrdinaryDiffEq.False())

    3rd order, 3-stage Explicit Runge-Kutta Method with optimal parameters.

    Like SSPRK methods, this method also takes optional arguments stage_limiter! and step_limiter!, where stage_limiter! and step_limiter! are functions of the form limiter!(u, integrator, p, t).

    The argument thread determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    Reference

    @article{Alshina2008, doi = {10.1134/s0965542508030068}, url = {https://doi.org/10.1134/s0965542508030068}, year = {2008}, month = mar, publisher = {Pleiades Publishing Ltd}, volume = {48}, number = {3}, pages = {395–405}, author = {E. A. Alshina and E. M. Zaks and N. N. Kalitkin}, title = {Optimal first- to sixth-order accurate Runge-Kutta schemes}, journal = {Computational Mathematics and Mathematical Physics} }

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    OrdinaryDiffEq.Alshina6 — Type
    Alshina6(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+         step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+         thread = OrdinaryDiffEq.False())

    6th order, 7-stage Explicit Runge-Kutta Method with optimal parameters.

    Like SSPRK methods, this method also takes optional arguments stage_limiter! and step_limiter!, where stage_limiter! and step_limiter! are functions of the form limiter!(u, integrator, p, t).

    The argument thread determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    Reference

    @article{Alshina2008, doi = {10.1134/s0965542508030068}, url = {https://doi.org/10.1134/s0965542508030068}, year = {2008}, month = mar, publisher = {Pleiades Publishing Ltd}, volume = {48}, number = {3}, pages = {395–405}, author = {E. A. Alshina and E. M. Zaks and N. N. Kalitkin}, title = {Optimal first- to sixth-order accurate Runge-Kutta schemes}, journal = {Computational Mathematics and Mathematical Physics} }

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    Lazy Interpolation Explicit Runge-Kutta Methods

    OrdinaryDiffEq.BS5 — Type
    BS5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        lazy = true)

    Explicit Runge-Kutta Method. Bogacki-Shampine 5/4 Runge-Kutta method. (lazy 5th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • lazy: determines if the lazy interpolant is used.

    References

    @article{bogacki1996efficient, title={An efficient runge-kutta (4, 5) pair}, author={Bogacki, P and Shampine, Lawrence F}, journal={Computers \& Mathematics with Applications}, volume={32}, number={6}, pages={15–28}, year={1996}, publisher={Elsevier} }

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    OrdinaryDiffEq.Vern6 — Type
    Vern6(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        lazy = true)

    Explicit Runge-Kutta Method. Verner's “Most Efficient” 6/5 Runge-Kutta method. (lazy 6th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • lazy: determines if the lazy interpolant is used.

    References

    @article{verner2010numerically, title={Numerically optimal Runge–Kutta pairs with interpolants}, author={Verner, James H}, journal={Numerical Algorithms}, volume={53}, number={2-3}, pages={383–396}, year={2010}, publisher={Springer} }

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    OrdinaryDiffEq.Vern7 — Type
    Vern7(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        lazy = true)

    Explicit Runge-Kutta Method. Verner's “Most Efficient” 7/6 Runge-Kutta method. (lazy 7th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • lazy: determines if the lazy interpolant is used.

    References

    @article{verner2010numerically, title={Numerically optimal Runge–Kutta pairs with interpolants}, author={Verner, James H}, journal={Numerical Algorithms}, volume={53}, number={2-3}, pages={383–396}, year={2010}, publisher={Springer} }

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    OrdinaryDiffEq.Vern8 — Type
    Vern8(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        lazy = true)

    Explicit Runge-Kutta Method. Verner's “Most Efficient” 8/7 Runge-Kutta method. (lazy 8th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • lazy: determines if the lazy interpolant is used.

    References

    @article{verner2010numerically, title={Numerically optimal Runge–Kutta pairs with interpolants}, author={Verner, James H}, journal={Numerical Algorithms}, volume={53}, number={2-3}, pages={383–396}, year={2010}, publisher={Springer} }

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    OrdinaryDiffEq.Vern9 — Type
    Vern9(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        lazy = true)

    Explicit Runge-Kutta Method. Verner's “Most Efficient” 9/8 Runge-Kutta method. (lazy9th order interpolant).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • lazy: determines if the lazy interpolant is used.

    References

    @article{verner2010numerically, title={Numerically optimal Runge–Kutta pairs with interpolants}, author={Verner, James H}, journal={Numerical Algorithms}, volume={53}, number={2-3}, pages={383–396}, year={2010}, publisher={Springer} }

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    Fixed Timestep Only Explicit Runge-Kutta Methods

    OrdinaryDiffEq.RK46NL — Type
    RK46NL(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. 6-stage, fourth order low-stage, low-dissipation, low-dispersion scheme. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Julien Berland, Christophe Bogey, Christophe Bailly. Low-Dissipation and Low-Dispersion Fourth-Order Runge-Kutta Algorithm. Computers & Fluids, 35(10), pp 1459-1463, 2006. doi: https://doi.org/10.1016/j.compfluid.2005.04.003

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    OrdinaryDiffEq.ORK256 — Type
    ORK256(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. A second-order, five-stage explicit Runge-Kutta method for wave propagation equations. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    Matteo Bernardini, Sergio Pirozzoli. A General Strategy for the Optimization of Runge-Kutta Schemes for Wave Propagation Phenomena. Journal of Computational Physics, 228(11), pp 4182-4199, 2009. doi: https://doi.org/10.1016/j.jcp.2009.02.032

    source

    Parallel Explicit Runge-Kutta Methods

    OrdinaryDiffEq.KuttaPRK2p5 — Type

    KuttaPRK2p5: Parallel Explicit Runge-Kutta Method A 5 parallel, 2 processor explicit Runge-Kutta method of 5th order.

    These methods utilize multithreading on the f calls to parallelize the problem. This requires that simultaneous calls to f are thread-safe.

    source
    diff --git a/previews/PR2081/nonstiff/lowstorage_ssprk/index.html b/previews/PR2081/nonstiff/lowstorage_ssprk/index.html new file mode 100644 index 0000000000..634d89e7cb --- /dev/null +++ b/previews/PR2081/nonstiff/lowstorage_ssprk/index.html @@ -0,0 +1,137 @@ + +PDE-Specialized Explicit Runge-Kutta Methods · OrdinaryDiffEq.jl
    Edit on GitHub

    PDE-Specialized Explicit Runge-Kutta Methods

    Low Storage Explicit Runge-Kutta Methods

    OrdinaryDiffEq.CarpenterKennedy2N54 — Type
    CarpenterKennedy2N54(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. A fourth-order, five-stage explicit low-storage method of Carpenter and Kennedy (free 3rd order Hermite interpolant). Fixed timestep only. Designed for hyperbolic PDEs (stability properties).

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    @article{carpenter1994fourth, title={Fourth-order 2N-storage Runge-Kutta schemes}, author={Carpenter, Mark H and Kennedy, Christopher A}, year={1994} }

    source
    OrdinaryDiffEq.SHLDDRK64 — Type
    SHLDDRK64(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. A fourth-order, six-stage explicit low-storage method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    D. Stanescu, W. G. Habashi. 2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational Acoustics. Journal of Computational Physics, 143(2), pp 674-681, 1998. doi: https://doi.org/10.1006/jcph.1998.5986 }

    source
    OrdinaryDiffEq.SHLDDRK52 — Type
    SHLDDRK52(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. TBD

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.SHLDDRK_2N — Type
    SHLDDRK_2N(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. TBD

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.HSLDDRK64 — Type
    HSLDDRK64(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. Low-Storage Method 6-stage, fourth order low-stage, low-dissipation, low-dispersion scheme. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    D. Stanescu, W. G. Habashi. 2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational Acoustics. Journal of Computational Physics, 143(2), pp 674-681, 1998. doi: https://doi.org/10.1006/jcph.1998.5986 }

    source
    OrdinaryDiffEq.DGLDDRK73_C — Type
    DGLDDRK73_C(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. 7-stage, third order low-storage low-dissipation, low-dispersion scheme for discontinuous Galerkin space discretizations applied to wave propagation problems. Optimized for PDE discretizations when maximum spatial step is small due to geometric features of computational domain. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    T. Toulorge, W. Desmet. Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations Applied to Wave Propagation Problems. Journal of Computational Physics, 231(4), pp 2067-2091, 2012. doi: https://doi.org/10.1016/j.jcp.2011.11.024

    source
    OrdinaryDiffEq.DGLDDRK84_C — Type
    DGLDDRK84_C(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. 8-stage, fourth order low-storage low-dissipation, low-dispersion scheme for discontinuous Galerkin space discretizations applied to wave propagation problems. Optimized for PDE discretizations when maximum spatial step is small due to geometric features of computational domain. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    T. Toulorge, W. Desmet. Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations Applied to Wave Propagation Problems. Journal of Computational Physics, 231(4), pp 2067-2091, 2012. doi: https://doi.org/10.1016/j.jcp.2011.11.024

    source
    OrdinaryDiffEq.DGLDDRK84_F — Type
    DGLDDRK84_F(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. 8-stage, fourth order low-storage low-dissipation, low-dispersion scheme for discontinuous Galerkin space discretizations applied to wave propagation problems. Optimized for PDE discretizations when the maximum spatial step size is not constrained. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    T. Toulorge, W. Desmet. Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations Applied to Wave Propagation Problems. Journal of Computational Physics, 231(4), pp 2067-2091, 2012. doi: https://doi.org/10.1016/j.jcp.2011.11.024

    source
    OrdinaryDiffEq.NDBLSRK124 — Type
    NDBLSRK124(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. 12-stage, fourth order low-storage method with optimized stability regions for advection-dominated problems. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    Jens Niegemann, Richard Diehl, Kurt Busch. Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. Journal of Computational Physics, 231, pp 364-372, 2012. doi: https://doi.org/10.1016/j.jcp.2011.09.003

    source
    OrdinaryDiffEq.NDBLSRK134 — Type
    NDBLSRK134(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. 13-stage, fourth order low-storage method with optimized stability regions for advection-dominated problems. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    Jens Niegemann, Richard Diehl, Kurt Busch. Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. Journal of Computational Physics, 231, pp 364-372, 2012. doi: https://doi.org/10.1016/j.jcp.2011.09.003

    source
    OrdinaryDiffEq.NDBLSRK144 — Type
    NDBLSRK144(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),
+        williamson_condition = true)

    Explicit Runge-Kutta Method. 14-stage, fourth order low-storage method with optimized stability regions for advection-dominated problems. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.
    • williamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.

    References

    Jens Niegemann, Richard Diehl, Kurt Busch. Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. Journal of Computational Physics, 231, pp 364-372, 2012. doi: https://doi.org/10.1016/j.jcp.2011.09.003

    source
    OrdinaryDiffEq.CFRLDDRK64 — Type
    CFRLDDRK64(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 6-stage, fourth order low-storage, low-dissipation, low-dispersion scheme. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    M. Calvo, J. M. Franco, L. Randez. A New Minimum Storage Runge–Kutta Scheme for Computational Acoustics. Journal of Computational Physics, 201, pp 1-12, 2004. doi: https://doi.org/10.1016/j.jcp.2004.05.012

    source
    OrdinaryDiffEq.TSLDDRK74 — Type
    TSLDDRK74(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 7-stage, fourth order low-storage low-dissipation, low-dispersion scheme with maximal accuracy and stability limit along the imaginary axes. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Kostas Tselios, T. E. Simos. Optimized Runge–Kutta Methods with Minimal Dispersion and Dissipation for Problems arising from Computational Acoustics. Physics Letters A, 393(1-2), pp 38-47, 2007. doi: https://doi.org/10.1016/j.physleta.2006.10.072

    source
    OrdinaryDiffEq.CKLLSRK43_2 — Type
    CKLLSRK43_2(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 4-stage, third order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK54_3C — Type
    CKLLSRK54_3C(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK95_4S — Type
    CKLLSRK95_4S(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK95_4C — Type
    CKLLSRK95_4C(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK95_4M — Type
    CKLLSRK95_4M(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK54_3C_3R — Type
    CKLLSRK54_3C_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK54_3M_3R — Type
    CKLLSRK54_3M_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK54_3N_3R — Type
    CKLLSRK54_3N_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK85_4C_3R — Type
    CKLLSRK85_4C_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK85_4M_3R — Type
    CKLLSRK85_4M_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK85_4P_3R — Type
    CKLLSRK85_4P_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK54_3N_4R — Type
    CKLLSRK54_3N_4R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK54_3M_4R — Type
    CKLLSRK54_3M_4R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK65_4M_4R — Type
    CKLLSRK65_4M_4R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. 6-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK85_4FM_4R — Type
    CKLLSRK85_4FM_4R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.CKLLSRK75_4M_5R — Type
    CKLLSRK75_4M_5R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. CKLLSRK754M5R: Low-Storage Method 7-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.ParsaniKetchesonDeconinck3S32 — Type
    ParsaniKetchesonDeconinck3S32(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 3-stage, second order (3S) low-storage scheme, optimized the spectral difference method applied to wave propagation problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Parsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899

    source
    OrdinaryDiffEq.ParsaniKetchesonDeconinck3S82 — Type
    ParsaniKetchesonDeconinck3S82(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 8-stage, second order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Parsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899

    source
    OrdinaryDiffEq.ParsaniKetchesonDeconinck3S53 — Type
    ParsaniKetchesonDeconinck3S53(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 5-stage, third order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Parsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899

    source
    OrdinaryDiffEq.ParsaniKetchesonDeconinck3S173 — Type
    ParsaniKetchesonDeconinck3S173(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 17-stage, third order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Parsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899

    source
    OrdinaryDiffEq.ParsaniKetchesonDeconinck3S94 — Type
    ParsaniKetchesonDeconinck3S94(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 9-stage, fourth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Parsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899

    source
    OrdinaryDiffEq.ParsaniKetchesonDeconinck3S184 — Type
    ParsaniKetchesonDeconinck3S184(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 18-stage, fourth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Parsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899

    source
    OrdinaryDiffEq.ParsaniKetchesonDeconinck3S105 — Type
    ParsaniKetchesonDeconinck3S105(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 10-stage, fifth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Parsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899

    source
    OrdinaryDiffEq.ParsaniKetchesonDeconinck3S205 — Type
    ParsaniKetchesonDeconinck3S205(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. Low-Storage Method 20-stage, fifth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Parsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899

    source
    OrdinaryDiffEq.RDPK3Sp35 — Type
    RDPK3Sp35(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, five-stage explicit Runge-Kutta method with embedded error estimator designed for spectral element discretizations of compressible fluid mechanics.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ranocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836

    source
    OrdinaryDiffEq.RDPK3SpFSAL35 — Type
    RDPK3SpFSAL35(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, five-stage explicit Runge-Kutta method with embedded error estimator using the FSAL property designed for spectral element discretizations of compressible fluid mechanics.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ranocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836

    source
    OrdinaryDiffEq.RDPK3Sp49 — Type
    RDPK3Sp49(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A fourth-order, nine-stage explicit Runge-Kutta method with embedded error estimator designed for spectral element discretizations of compressible fluid mechanics.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ranocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836

    source
    OrdinaryDiffEq.RDPK3SpFSAL49 — Type
    RDPK3SpFSAL49(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A fourth-order, nine-stage explicit Runge-Kutta method with embedded error estimator using the FSAL property designed for spectral element discretizations of compressible fluid mechanics.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ranocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836

    source
    OrdinaryDiffEq.RDPK3Sp510 — Type
    RDPK3Sp510(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A fifth-order, ten-stage explicit Runge-Kutta method with embedded error estimator designed for spectral element discretizations of compressible fluid mechanics.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ranocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836

    source
    OrdinaryDiffEq.RDPK3SpFSAL510 — Type
    RDPK3SpFSAL510(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A fifth-order, ten-stage explicit Runge-Kutta method with embedded error estimator using the FSAL property designed for spectral element discretizations of compressible fluid mechanics.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ranocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836

    source

    SSP Optimized Runge-Kutta Methods

    OrdinaryDiffEq.KYK2014DGSSPRK_3S2 — Type
    KYK2014DGSSPRK_3S2(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. TBD

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.SSPRK22 — Type
    SSPRK22(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A second-order, two-stage explicit strong stability preserving (SSP) method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Shu, Chi-Wang, and Stanley Osher. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics 77.2 (1988): 439-471. https://doi.org/10.1016/0021-9991(88)90177-5

    source
    OrdinaryDiffEq.SSPRK33 — Type
    SSPRK33(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, three-stage explicit strong stability preserving (SSP) method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Shu, Chi-Wang, and Stanley Osher. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics 77.2 (1988): 439-471. https://doi.org/10.1016/0021-9991(88)90177-5

    source
    OrdinaryDiffEq.SSPRK53 — Type
    SSPRK53(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, five-stage explicit strong stability preserving (SSP) method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ruuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207

    source
    OrdinaryDiffEq.KYKSSPRK42 — Type
    KYKSSPRK42(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. TBD

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    source
    OrdinaryDiffEq.SSPRK53_2N1 — Type
    SSPRK53_2N1(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Higueras and T. Roldán. New third order low-storage SSP explicit Runge–Kutta methods arXiv:1809.04807v1.

    source
    OrdinaryDiffEq.SSPRK53_2N2 — Type
    SSPRK53_2N2(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Higueras and T. Roldán. New third order low-storage SSP explicit Runge–Kutta methods arXiv:1809.04807v1.

    source
    OrdinaryDiffEq.SSPRK53_H — Type
    SSPRK53_H(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Higueras and T. Roldán. New third order low-storage SSP explicit Runge–Kutta methods arXiv:1809.04807v1.

    source
    OrdinaryDiffEq.SSPRK63 — Type
    SSPRK63(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, six-stage explicit strong stability preserving (SSP) method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ruuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207

    source
    OrdinaryDiffEq.SSPRK73 — Type
    SSPRK73(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, seven-stage explicit strong stability preserving (SSP) method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ruuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207

    source
    OrdinaryDiffEq.SSPRK83 — Type
    SSPRK83(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, eight-stage explicit strong stability preserving (SSP) method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ruuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207

    source
    OrdinaryDiffEq.SSPRK43 — Type
    SSPRK43(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, four-stage explicit strong stability preserving (SSP) method.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Optimal third-order explicit SSP method with four stages discovered by

    • J. F. B. M. Kraaijevanger. "Contractivity of Runge-Kutta methods." In: BIT Numerical Mathematics 31.3 (1991), pp. 482–528. DOI: 10.1007/BF01933264.

    Embedded method constructed by

    • Sidafa Conde, Imre Fekete, John N. Shadid. "Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving Runge–Kutta methods." arXiv: 1806.08693

    Efficient implementation (and optimized controller) developed by

    • Hendrik Ranocha, Lisandro Dalcin, Matteo Parsani, David I. Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836
    source
    OrdinaryDiffEq.SSPRK432 — Type
    SSPRK432(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, four-stage explicit strong stability preserving (SSP) method.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Gottlieb, Sigal, David I. Ketcheson, and Chi-Wang Shu. Strong stability preserving Runge-Kutta and multistep time discretizations. World Scientific, 2011. Example 6.1

    source
    OrdinaryDiffEq.SSPRKMSVS43 — Type
    SSPRKMSVS43(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, four-step explicit strong stability preserving (SSP) linear multistep method. This method does not come with an error estimator and requires a fixed time step size.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Shu, Chi-Wang. Total-variation-diminishing time discretizations. SIAM Journal on Scientific and Statistical Computing 9, no. 6 (1988): 1073-1084. DOI: 10.1137/0909073

    source
    OrdinaryDiffEq.SSPRKMSVS32 — Type
    SSPRKMSVS32(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A second-order, three-step explicit strong stability preserving (SSP) linear multistep method. This method does not come with an error estimator and requires a fixed time step size.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Shu, Chi-Wang. Total-variation-diminishing time discretizations. SIAM Journal on Scientific and Statistical Computing 9, no. 6 (1988): 1073-1084. DOI: 10.1137/0909073

    source
    OrdinaryDiffEq.SSPRK932 — Type
    SSPRK932(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A third-order, nine-stage explicit strong stability preserving (SSP) method.

    Consider using SSPRK43 instead, which uses the same main method and an improved embedded method.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Gottlieb, Sigal, David I. Ketcheson, and Chi-Wang Shu. Strong stability preserving Runge-Kutta and multistep time discretizations. World Scientific, 2011.

    source
    OrdinaryDiffEq.SSPRK54 — Type
    SSPRK54(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A fourth-order, five-stage explicit strong stability preserving (SSP) method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ruuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207.

    source
    OrdinaryDiffEq.SSPRK104 — Type
    SSPRK104(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        step_limiter! = OrdinaryDiffEq.trivial_limiter!,
+        thread = OrdinaryDiffEq.False(),)

    Explicit Runge-Kutta Method. A fourth-order, ten-stage explicit strong stability preserving (SSP) method. Fixed timestep only.

    Keyword Arguments

    • stage_limiter!: function of the form limiter!(u, integrator, p, t)
    • step_limiter!: function of the form limiter!(u, integrator, p, t)
    • thread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.

    References

    Ketcheson, David I. Highly efficient strong stability-preserving Runge–Kutta methods with low-storage implementations. SIAM Journal on Scientific Computing 30.4 (2008): 2113-2136.

    source
    diff --git a/previews/PR2081/nonstiff/nonstiff_multistep/index.html b/previews/PR2081/nonstiff/nonstiff_multistep/index.html new file mode 100644 index 0000000000..98ea06b545 --- /dev/null +++ b/previews/PR2081/nonstiff/nonstiff_multistep/index.html @@ -0,0 +1,6 @@ + +Multistep Methods for Non-Stiff Equations · OrdinaryDiffEq.jl
    Edit on GitHub

    Multistep Methods for Non-Stiff Equations

    Explicit Multistep Methods

    OrdinaryDiffEq.AB3 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    AB3: Adams-Bashforth Explicit Method The 3-step third order multistep method. Ralston's Second Order Method is used to calculate starting values.

    source
    OrdinaryDiffEq.AB4 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    AB4: Adams-Bashforth Explicit Method The 4-step fourth order multistep method. Runge-Kutta method of order 4 is used to calculate starting values.

    source
    OrdinaryDiffEq.AB5 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    AB5: Adams-Bashforth Explicit Method The 3-step third order multistep method. Ralston's Second Order Method is used to calculate starting values.

    source
    OrdinaryDiffEq.AN5 — Type

    AN5: Adaptive step size Adams explicit Method An adaptive 5th order fixed-leading coefficient Adams method in Nordsieck form.

    source

    Predictor-Corrector Methods

    OrdinaryDiffEq.ABM32 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    ABM32: Adams-Bashforth Explicit Method It is third order method. In ABM32, AB3 works as predictor and Adams Moulton 2-steps method works as Corrector. Ralston's Second Order Method is used to calculate starting values.

    source
    OrdinaryDiffEq.ABM43 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    ABM43: Adams-Bashforth Explicit Method It is fourth order method. In ABM43, AB4 works as predictor and Adams Moulton 3-steps method works as Corrector. Runge-Kutta method of order 4 is used to calculate starting values.

    source
    OrdinaryDiffEq.ABM54 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    ABM54: Adams-Bashforth Explicit Method It is fifth order method. In ABM54, AB5 works as predictor and Adams Moulton 4-steps method works as Corrector. Runge-Kutta method of order 4 is used to calculate starting values.

    source
    OrdinaryDiffEq.VCAB3 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    VCAB3: Adaptive step size Adams explicit Method The 3rd order Adams method. Bogacki-Shampine 3/2 method is used to calculate starting values.

    source
    OrdinaryDiffEq.VCAB4 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    VCAB4: Adaptive step size Adams explicit Method The 4th order Adams method. Runge-Kutta 4 is used to calculate starting values.

    source
    OrdinaryDiffEq.VCAB5 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    VCAB5: Adaptive step size Adams explicit Method The 5th order Adams method. Runge-Kutta 4 is used to calculate starting values.

    source
    OrdinaryDiffEq.VCABM3 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    VCABM3: Adaptive step size Adams explicit Method The 3rd order Adams-Moulton method. Bogacki-Shampine 3/2 method is used to calculate starting values.

    source
    OrdinaryDiffEq.VCABM4 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    VCABM4: Adaptive step size Adams explicit Method The 4th order Adams-Moulton method. Runge-Kutta 4 is used to calculate starting values.

    source
    OrdinaryDiffEq.VCABM5 — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    VCABM5: Adaptive step size Adams explicit Method The 5th order Adams-Moulton method. Runge-Kutta 4 is used to calculate starting values.

    source
    OrdinaryDiffEq.VCABM — Type

    E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1

    VCABM: Adaptive step size Adams explicit Method An adaptive order adaptive time Adams Moulton method. It uses an order adaptivity algorithm is derived from Shampine's DDEABM.

    source
    diff --git a/previews/PR2081/search/index.html b/previews/PR2081/search/index.html new file mode 100644 index 0000000000..6f05cf74a8 --- /dev/null +++ b/previews/PR2081/search/index.html @@ -0,0 +1,6 @@ + +Search · OrdinaryDiffEq.jl diff --git a/previews/PR2081/search_index.js b/previews/PR2081/search_index.js new file mode 100644 index 0000000000..fc41b7181b --- /dev/null +++ b/previews/PR2081/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"nonstiff/explicitrk/#Explicit-Runge-Kutta-Methods","page":"Explicit Runge-Kutta Methods","title":"Explicit Runge-Kutta Methods","text":"","category":"section"},{"location":"nonstiff/explicitrk/","page":"Explicit Runge-Kutta Methods","title":"Explicit Runge-Kutta Methods","text":"With the help of FastBroadcast.jl, we can use threaded parallelism to reduce compute time for all of the explicit Runge-Kutta methods! The thread option determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads. When we call solve(prob, alg(thread=OrdinaryDiffEq.True())), we can turn on the multithreading option to achieve acceleration (for sufficiently large problems).","category":"page"},{"location":"nonstiff/explicitrk/#Standard-Explicit-Runge-Kutta-Methods","page":"Explicit Runge-Kutta Methods","title":"Standard Explicit Runge-Kutta Methods","text":"","category":"section"},{"location":"nonstiff/explicitrk/","page":"Explicit Runge-Kutta Methods","title":"Explicit Runge-Kutta Methods","text":"Heun\r\nRalston\r\nMidpoint\r\nRK4\r\nRKM\r\nMSRK5\r\nMSRK6\r\nAnas5\r\nRKO65\r\nOwrenZen3\r\nOwrenZen4\r\nOwrenZen5\r\nBS3\r\nDP5\r\nTsit5\r\nDP8\r\nTanYam7\r\nTsitPap8\r\nFeagin10\r\nFeagin12\r\nFeagin14\r\nFRK65\r\nPFRK87\r\nStepanov5\r\nSIR54\r\nAlshina2\r\nAlshina3\r\nAlshina6","category":"page"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Heun","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Heun","text":"Heun(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. The second order Heun's method. Uses embedded Euler method for adaptivity.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Ralston","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Ralston","text":"Ralston(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. The optimized second order midpoint method. Uses embedded Euler method for adaptivity.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Midpoint","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Midpoint","text":"Midpoint(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. The second order midpoint method. Uses embedded Euler method for adaptivity.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.RK4","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RK4","text":"RK4(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. The canonical Runge-Kutta Order 4 method. Uses a defect control for adaptive stepping using maximum error over the whole interval.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n@article{shampine2005solving, title={Solving ODEs and DDEs with residual control}, author={Shampine, LF}, journal={Applied Numerical Mathematics}, volume={52}, number={1}, pages={113–127}, year={2005}, publisher={Elsevier} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.RKM","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RKM","text":"RKM(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. TBD\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.MSRK5","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.MSRK5","text":"MSRK5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. 5th order Explicit RK method.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nMisha Stepanov - https://arxiv.org/pdf/2202.08443.pdf : Figure 3.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.MSRK6","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.MSRK6","text":"MSRK6(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. 6th order Explicit RK method.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nMisha Stepanov - https://arxiv.org/pdf/2202.08443.pdf : Table4\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Anas5","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Anas5","text":"Anas5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n w = 1)\n\nExplicit Runge-Kutta Method. 4th order Runge-Kutta method designed for periodic problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nw: a periodicity estimate, which when accurate the method becomes 5th order (and is otherwise 4th order with less error for better estimates).\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.RKO65","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RKO65","text":"RKO5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. 5th order Explicit RK method.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nTsitouras, Ch. \"Explicit Runge–Kutta methods for starting integration of Lane–Emden problem.\" Applied Mathematics and Computation 354 (2019): 353-364. doi: https://doi.org/10.1016/j.amc.2019.02.047\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.OwrenZen3","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.OwrenZen3","text":"OwrenZen3(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Owren-Zennaro optimized interpolation 3/2 method (free 3rd order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n@article{owren1992derivation, title={Derivation of efficient, continuous, explicit Runge–Kutta methods}, author={Owren, Brynjulf and Zennaro, Marino}, journal={SIAM journal on scientific and statistical computing}, volume={13}, number={6}, pages={1488–1501}, year={1992}, publisher={SIAM} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.OwrenZen4","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.OwrenZen4","text":"OwrenZen4(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Owren-Zennaro optimized interpolation 4/3 method (free 4th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n@article{owren1992derivation, title={Derivation of efficient, continuous, explicit Runge–Kutta methods}, author={Owren, Brynjulf and Zennaro, Marino}, journal={SIAM journal on scientific and statistical computing}, volume={13}, number={6}, pages={1488–1501}, year={1992}, publisher={SIAM} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.OwrenZen5","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.OwrenZen5","text":"OwrenZen5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Owren-Zennaro optimized interpolation 5/4 method (free 5th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n@article{owren1992derivation, title={Derivation of efficient, continuous, explicit Runge–Kutta methods}, author={Owren, Brynjulf and Zennaro, Marino}, journal={SIAM journal on scientific and statistical computing}, volume={13}, number={6}, pages={1488–1501}, year={1992}, publisher={SIAM} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.BS3","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.BS3","text":"BS3(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, four-stage explicit FSAL Runge-Kutta method with embedded error estimator of Bogacki and Shampine.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n@article{bogacki19893, title={A 3 (2) pair of Runge-Kutta formulas}, author={Bogacki, Przemyslaw and Shampine, Lawrence F}, journal={Applied Mathematics Letters}, volume={2}, number={4}, pages={321–325}, year={1989}, publisher={Elsevier} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.DP5","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.DP5","text":"DP5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Dormand-Prince's 5/4 Runge-Kutta method. (free 4th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n@article{dormand1980family, title={A family of embedded Runge-Kutta formulae}, author={Dormand, John R and Prince, Peter J}, journal={Journal of computational and applied mathematics}, volume={6}, number={1}, pages={19–26}, year={1980}, publisher={Elsevier} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Tsit5","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Tsit5","text":"Tsit5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A fifth-order explicit Runge-Kutta method with embedded error estimator of Tsitouras. Free 4th order interpolant.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n@article{tsitouras2011runge, title={Runge–Kutta pairs of order 5 (4) satisfying only the first column simplifying assumption}, author={Tsitouras, Ch}, journal={Computers \\& Mathematics with Applications}, volume={62}, number={2}, pages={770–775}, year={2011}, publisher={Elsevier} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.DP8","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.DP8","text":"DP8(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Hairer's 8/5/3 adaption of the Dormand-Prince Runge-Kutta method. (7th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nE. Hairer, S.P. Norsett, G. Wanner, (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series in Computational Mathematics, Springer-Verlag.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.TanYam7","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.TanYam7","text":"TanYam7(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Tanaka-Yamashita 7 Runge-Kutta method. (7th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nTanaka M., Muramatsu S., Yamashita S., (1992), On the Optimization of Some Nine-Stage Seventh-order Runge-Kutta Method, Information Processing Society of Japan, 33 (12), pp. 1512-1526.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.TsitPap8","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.TsitPap8","text":"TsitPap8(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Tsitouras-Papakostas 8/7 Runge-Kutta method.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Feagin10","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Feagin10","text":"@article{feagin2012high, title={High-order explicit Runge-Kutta methods using m-symmetry}, author={Feagin, Terry}, year={2012}, publisher={Neural, Parallel \\& Scientific Computations} }\n\nFeagin10: Explicit Runge-Kutta Method Feagin's 10th-order Runge-Kutta method.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Feagin12","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Feagin12","text":"@article{feagin2012high, title={High-order explicit Runge-Kutta methods using m-symmetry}, author={Feagin, Terry}, year={2012}, publisher={Neural, Parallel \\& Scientific Computations} }\n\nFeagin12: Explicit Runge-Kutta Method Feagin's 12th-order Runge-Kutta method.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Feagin14","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Feagin14","text":"Feagin, T., “An Explicit Runge-Kutta Method of Order Fourteen,” Numerical Algorithms, 2009\n\nFeagin14: Explicit Runge-Kutta Method Feagin's 14th-order Runge-Kutta method.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.FRK65","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.FRK65","text":"FRK65(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n omega = 0.0)\n\nExplicit Runge-Kutta Method. Zero Dissipation Runge-Kutta of 6th order.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nomega: a periodicity phase estimate, when accurate this method results in zero numerical dissipation.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.PFRK87","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.PFRK87","text":"PFRK87(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n omega = 0.0)\n\nExplicit Runge-Kutta Method. Phase-fitted Runge-Kutta of 8th order.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nomega: a periodicity phase estimate, when accurate this method results in zero numerical dissipation.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Stepanov5","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Stepanov5","text":"Stepanov5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. 5th order Explicit RK method.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n@article{Stepanov2021Embedded5, title={Embedded (4, 5) pairs of explicit 7-stage Runge–Kutta methods with FSAL property}, author={Misha Stepanov}, journal={Calcolo}, year={2021}, volume={59} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.SIR54","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SIR54","text":"SIR54(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False())\n\n5th order Explicit RK method suited for SIR-type epidemic models.\n\nLike SSPRK methods, this method also takes optional arguments stage_limiter! and step_limiter!, where stage_limiter! and step_limiter! are functions of the form limiter!(u, integrator, p, t).\n\nThe argument thread determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReference\n\n@article{Kovalnogov2020RungeKuttaPS, title={Runge–Kutta pairs suited for SIR‐type epidemic models}, author={Vladislav N. Kovalnogov and Theodore E. Simos and Ch. Tsitouras}, journal={Mathematical Methods in the Applied Sciences}, year={2020}, volume={44}, pages={5210 - 5216} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Alshina2","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Alshina2","text":"Alshina2(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False())\n\n2nd order, 2-stage Explicit Runge-Kutta Method with optimal parameters.\n\nLike SSPRK methods, this method also takes optional arguments stage_limiter! and step_limiter!, where stage_limiter! and step_limiter! are functions of the form limiter!(u, integrator, p, t).\n\nThe argument thread determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReference\n\n@article{Alshina2008, doi = {10.1134/s0965542508030068}, url = {https://doi.org/10.1134/s0965542508030068}, year = {2008}, month = mar, publisher = {Pleiades Publishing Ltd}, volume = {48}, number = {3}, pages = {395–405}, author = {E. A. Alshina and E. M. Zaks and N. N. Kalitkin}, title = {Optimal first- to sixth-order accurate Runge-Kutta schemes}, journal = {Computational Mathematics and Mathematical Physics} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Alshina3","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Alshina3","text":"Alshina3(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False())\n\n3rd order, 3-stage Explicit Runge-Kutta Method with optimal parameters.\n\nLike SSPRK methods, this method also takes optional arguments stage_limiter! and step_limiter!, where stage_limiter! and step_limiter! are functions of the form limiter!(u, integrator, p, t).\n\nThe argument thread determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReference\n\n@article{Alshina2008, doi = {10.1134/s0965542508030068}, url = {https://doi.org/10.1134/s0965542508030068}, year = {2008}, month = mar, publisher = {Pleiades Publishing Ltd}, volume = {48}, number = {3}, pages = {395–405}, author = {E. A. Alshina and E. M. Zaks and N. N. Kalitkin}, title = {Optimal first- to sixth-order accurate Runge-Kutta schemes}, journal = {Computational Mathematics and Mathematical Physics} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Alshina6","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Alshina6","text":"Alshina6(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False())\n\n6th order, 7-stage Explicit Runge-Kutta Method with optimal parameters.\n\nLike SSPRK methods, this method also takes optional arguments stage_limiter! and step_limiter!, where stage_limiter! and step_limiter! are functions of the form limiter!(u, integrator, p, t).\n\nThe argument thread determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReference\n\n@article{Alshina2008, doi = {10.1134/s0965542508030068}, url = {https://doi.org/10.1134/s0965542508030068}, year = {2008}, month = mar, publisher = {Pleiades Publishing Ltd}, volume = {48}, number = {3}, pages = {395–405}, author = {E. A. Alshina and E. M. Zaks and N. N. Kalitkin}, title = {Optimal first- to sixth-order accurate Runge-Kutta schemes}, journal = {Computational Mathematics and Mathematical Physics} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#Lazy-Interpolation-Explicit-Runge-Kutta-Methods","page":"Explicit Runge-Kutta Methods","title":"Lazy Interpolation Explicit Runge-Kutta Methods","text":"","category":"section"},{"location":"nonstiff/explicitrk/","page":"Explicit Runge-Kutta Methods","title":"Explicit Runge-Kutta Methods","text":"BS5\r\nVern6\r\nVern7\r\nVern8\r\nVern9","category":"page"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.BS5","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.BS5","text":"BS5(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n lazy = true)\n\nExplicit Runge-Kutta Method. Bogacki-Shampine 5/4 Runge-Kutta method. (lazy 5th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nlazy: determines if the lazy interpolant is used.\n\nReferences\n\n@article{bogacki1996efficient, title={An efficient runge-kutta (4, 5) pair}, author={Bogacki, P and Shampine, Lawrence F}, journal={Computers \\& Mathematics with Applications}, volume={32}, number={6}, pages={15–28}, year={1996}, publisher={Elsevier} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Vern6","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Vern6","text":"Vern6(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n lazy = true)\n\nExplicit Runge-Kutta Method. Verner's “Most Efficient” 6/5 Runge-Kutta method. (lazy 6th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nlazy: determines if the lazy interpolant is used.\n\nReferences\n\n@article{verner2010numerically, title={Numerically optimal Runge–Kutta pairs with interpolants}, author={Verner, James H}, journal={Numerical Algorithms}, volume={53}, number={2-3}, pages={383–396}, year={2010}, publisher={Springer} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Vern7","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Vern7","text":"Vern7(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n lazy = true)\n\nExplicit Runge-Kutta Method. Verner's “Most Efficient” 7/6 Runge-Kutta method. (lazy 7th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nlazy: determines if the lazy interpolant is used.\n\nReferences\n\n@article{verner2010numerically, title={Numerically optimal Runge–Kutta pairs with interpolants}, author={Verner, James H}, journal={Numerical Algorithms}, volume={53}, number={2-3}, pages={383–396}, year={2010}, publisher={Springer} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Vern8","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Vern8","text":"Vern8(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n lazy = true)\n\nExplicit Runge-Kutta Method. Verner's “Most Efficient” 8/7 Runge-Kutta method. (lazy 8th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nlazy: determines if the lazy interpolant is used.\n\nReferences\n\n@article{verner2010numerically, title={Numerically optimal Runge–Kutta pairs with interpolants}, author={Verner, James H}, journal={Numerical Algorithms}, volume={53}, number={2-3}, pages={383–396}, year={2010}, publisher={Springer} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Vern9","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Vern9","text":"Vern9(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n lazy = true)\n\nExplicit Runge-Kutta Method. Verner's “Most Efficient” 9/8 Runge-Kutta method. (lazy9th order interpolant).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nlazy: determines if the lazy interpolant is used.\n\nReferences\n\n@article{verner2010numerically, title={Numerically optimal Runge–Kutta pairs with interpolants}, author={Verner, James H}, journal={Numerical Algorithms}, volume={53}, number={2-3}, pages={383–396}, year={2010}, publisher={Springer} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#Fixed-Timestep-Only-Explicit-Runge-Kutta-Methods","page":"Explicit Runge-Kutta Methods","title":"Fixed Timestep Only Explicit Runge-Kutta Methods","text":"","category":"section"},{"location":"nonstiff/explicitrk/","page":"Explicit Runge-Kutta Methods","title":"Explicit Runge-Kutta Methods","text":"Euler\r\nRK46NL\r\nORK256","category":"page"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.Euler","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.Euler","text":"Euler - The canonical forward Euler method. Fixed timestep only.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.RK46NL","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RK46NL","text":"RK46NL(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. 6-stage, fourth order low-stage, low-dissipation, low-dispersion scheme. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nJulien Berland, Christophe Bogey, Christophe Bailly. Low-Dissipation and Low-Dispersion Fourth-Order Runge-Kutta Algorithm. Computers & Fluids, 35(10), pp 1459-1463, 2006. doi: https://doi.org/10.1016/j.compfluid.2005.04.003\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.ORK256","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ORK256","text":"ORK256(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. A second-order, five-stage explicit Runge-Kutta method for wave propagation equations. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nMatteo Bernardini, Sergio Pirozzoli. A General Strategy for the Optimization of Runge-Kutta Schemes for Wave Propagation Phenomena. Journal of Computational Physics, 228(11), pp 4182-4199, 2009. doi: https://doi.org/10.1016/j.jcp.2009.02.032\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicitrk/#Parallel-Explicit-Runge-Kutta-Methods","page":"Explicit Runge-Kutta Methods","title":"Parallel Explicit Runge-Kutta Methods","text":"","category":"section"},{"location":"nonstiff/explicitrk/","page":"Explicit Runge-Kutta Methods","title":"Explicit Runge-Kutta Methods","text":"KuttaPRK2p5","category":"page"},{"location":"nonstiff/explicitrk/#OrdinaryDiffEq.KuttaPRK2p5","page":"Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.KuttaPRK2p5","text":"KuttaPRK2p5: Parallel Explicit Runge-Kutta Method A 5 parallel, 2 processor explicit Runge-Kutta method of 5th order.\n\nThese methods utilize multithreading on the f calls to parallelize the problem. This requires that simultaneous calls to f are thread-safe.\n\n\n\n\n\n","category":"type"},{"location":"semilinear/magnus/#Magnus-and-Lie-Group-Integrators","page":"Magnus and Lie Group Integrators","title":"Magnus and Lie Group Integrators","text":"","category":"section"},{"location":"semilinear/magnus/","page":"Magnus and Lie Group Integrators","title":"Magnus and Lie Group Integrators","text":"MagnusMidpoint\r\nMagnusLeapfrog\r\nLieEuler\r\nMagnusGauss4\r\nMagnusNC6\r\nMagnusGL6\r\nMagnusGL8\r\nMagnusNC8\r\nMagnusGL4\r\nRKMK2\r\nRKMK4\r\nLieRK4\r\nCG2\r\nCG3\r\nCG4a\r\nMagnusAdapt4\r\nCayleyEuler","category":"page"},{"location":"stiff/stiff_multistep/#Multistep-Methods-for-Stiff-Equations","page":"Multistep Methods for Stiff Equations","title":"Multistep Methods for Stiff Equations","text":"","category":"section"},{"location":"stiff/stiff_multistep/","page":"Multistep Methods for Stiff Equations","title":"Multistep Methods for Stiff Equations","text":"QNDF1\r\nQBDF1\r\nQNDF2\r\nQBDF2\r\nABDF2\r\nQNDF\r\nQBDF\r\nFBDF\r\nMEBDF2","category":"page"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.QNDF1","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.QNDF1","text":"QNDF1: Multistep Method An adaptive order 1 quasi-constant timestep L-stable numerical differentiation function (NDF) method. Optional parameter kappa defaults to Shampine's accuracy-optimal -0.1850.\n\nSee also QNDF.\n\n\n\n\n\n","category":"type"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.QBDF1","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.QBDF1","text":"QBDF1: Multistep Method\n\nAn alias of QNDF1 with κ=0.\n\n\n\n\n\n","category":"function"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.QNDF2","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.QNDF2","text":"QNDF2: Multistep Method An adaptive order 2 quasi-constant timestep L-stable numerical differentiation function (NDF) method.\n\nSee also QNDF.\n\n\n\n\n\n","category":"type"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.QBDF2","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.QBDF2","text":"QBDF2: Multistep Method\n\nAn alias of QNDF2 with κ=0.\n\n\n\n\n\n","category":"function"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.ABDF2","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.ABDF2","text":"E. Alberdi Celayaa, J. J. Anza Aguirrezabalab, P. Chatzipantelidisc. Implementation of an Adaptive BDF2 Formula and Comparison with The MATLAB Ode15s. Procedia Computer Science, 29, pp 1014-1026, 2014. doi: https://doi.org/10.1016/j.procs.2014.05.091\n\nABDF2: Multistep Method An adaptive order 2 L-stable fixed leading coefficient multistep BDF method.\n\n\n\n\n\n","category":"type"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.QNDF","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.QNDF","text":"QNDF: Multistep Method An adaptive order quasi-constant timestep NDF method. Utilizes Shampine's accuracy-optimal kappa values as defaults (has a keyword argument for a tuple of kappa coefficients).\n\n@article{shampine1997matlab, title={The matlab ode suite}, author={Shampine, Lawrence F and Reichelt, Mark W}, journal={SIAM journal on scientific computing}, volume={18}, number={1}, pages={1–22}, year={1997}, publisher={SIAM} }\n\n\n\n\n\n","category":"type"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.QBDF","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.QBDF","text":"QBDF: Multistep Method\n\nAn alias of QNDF with κ=0.\n\n\n\n\n\n","category":"function"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.FBDF","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.FBDF","text":"FBDF: Fixed leading coefficient BDF\n\nAn adaptive order quasi-constant timestep NDF method. Utilizes Shampine's accuracy-optimal kappa values as defaults (has a keyword argument for a tuple of kappa coefficients).\n\n@article{shampine2002solving, title={Solving 0= F (t, y (t), y′(t)) in Matlab}, author={Shampine, Lawrence F}, year={2002}, publisher={Walter de Gruyter GmbH \\& Co. KG} }\n\n\n\n\n\n","category":"type"},{"location":"stiff/stiff_multistep/#OrdinaryDiffEq.MEBDF2","page":"Multistep Methods for Stiff Equations","title":"OrdinaryDiffEq.MEBDF2","text":"MEBDF2: Multistep Method The second order Modified Extended BDF method, which has improved stability properties over the standard BDF. Fixed timestep only.\n\n\n\n\n\n","category":"type"},{"location":"dae/fully_implicit/#Methods-for-Fully-Implicit-ODEs-(DAEProblem)","page":"Methods for Fully Implicit ODEs (DAEProblem)","title":"Methods for Fully Implicit ODEs (DAEProblem)","text":"","category":"section"},{"location":"dae/fully_implicit/","page":"Methods for Fully Implicit ODEs (DAEProblem)","title":"Methods for Fully Implicit ODEs (DAEProblem)","text":"DImplicitEuler\r\nDABDF2\r\nDFBDF","category":"page"},{"location":"nonstiff/lowstorage_ssprk/#PDE-Specialized-Explicit-Runge-Kutta-Methods","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"PDE-Specialized Explicit Runge-Kutta Methods","text":"","category":"section"},{"location":"nonstiff/lowstorage_ssprk/#Low-Storage-Explicit-Runge-Kutta-Methods","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"Low Storage Explicit Runge-Kutta Methods","text":"","category":"section"},{"location":"nonstiff/lowstorage_ssprk/","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"PDE-Specialized Explicit Runge-Kutta Methods","text":"CarpenterKennedy2N54\r\nSHLDDRK64\r\nSHLDDRK52\r\nSHLDDRK_2N\r\nHSLDDRK64\r\nDGLDDRK73_C\r\nDGLDDRK84_C\r\nDGLDDRK84_F\r\nNDBLSRK124\r\nNDBLSRK134\r\nNDBLSRK144\r\nCFRLDDRK64\r\nTSLDDRK74\r\nCKLLSRK43_2\r\nCKLLSRK54_3C\r\nCKLLSRK95_4S\r\nCKLLSRK95_4C\r\nCKLLSRK95_4M\r\nCKLLSRK54_3C_3R\r\nCKLLSRK54_3M_3R\r\nCKLLSRK54_3N_3R\r\nCKLLSRK85_4C_3R\r\nCKLLSRK85_4M_3R\r\nCKLLSRK85_4P_3R\r\nCKLLSRK54_3N_4R\r\nCKLLSRK54_3M_4R\r\nCKLLSRK65_4M_4R\r\nCKLLSRK85_4FM_4R\r\nCKLLSRK75_4M_5R\r\nParsaniKetchesonDeconinck3S32\r\nParsaniKetchesonDeconinck3S82\r\nParsaniKetchesonDeconinck3S53\r\nParsaniKetchesonDeconinck3S173\r\nParsaniKetchesonDeconinck3S94\r\nParsaniKetchesonDeconinck3S184\r\nParsaniKetchesonDeconinck3S105\r\nParsaniKetchesonDeconinck3S205\r\nRDPK3Sp35\r\nRDPK3SpFSAL35\r\nRDPK3Sp49\r\nRDPK3SpFSAL49\r\nRDPK3Sp510\r\nRDPK3SpFSAL510","category":"page"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CarpenterKennedy2N54","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CarpenterKennedy2N54","text":"CarpenterKennedy2N54(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. A fourth-order, five-stage explicit low-storage method of Carpenter and Kennedy (free 3rd order Hermite interpolant). Fixed timestep only. Designed for hyperbolic PDEs (stability properties).\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\n@article{carpenter1994fourth, title={Fourth-order 2N-storage Runge-Kutta schemes}, author={Carpenter, Mark H and Kennedy, Christopher A}, year={1994} }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SHLDDRK64","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SHLDDRK64","text":"SHLDDRK64(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. A fourth-order, six-stage explicit low-storage method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nD. Stanescu, W. G. Habashi. 2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational Acoustics. Journal of Computational Physics, 143(2), pp 674-681, 1998. doi: https://doi.org/10.1006/jcph.1998.5986 }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SHLDDRK52","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SHLDDRK52","text":"SHLDDRK52(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. TBD\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SHLDDRK_2N","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SHLDDRK_2N","text":"SHLDDRK_2N(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. TBD\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.HSLDDRK64","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.HSLDDRK64","text":"HSLDDRK64(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. Low-Storage Method 6-stage, fourth order low-stage, low-dissipation, low-dispersion scheme. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nD. Stanescu, W. G. Habashi. 2N-Storage Low Dissipation and Dispersion Runge-Kutta Schemes for Computational Acoustics. Journal of Computational Physics, 143(2), pp 674-681, 1998. doi: https://doi.org/10.1006/jcph.1998.5986 }\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.DGLDDRK73_C","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.DGLDDRK73_C","text":"DGLDDRK73_C(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. 7-stage, third order low-storage low-dissipation, low-dispersion scheme for discontinuous Galerkin space discretizations applied to wave propagation problems. Optimized for PDE discretizations when maximum spatial step is small due to geometric features of computational domain. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nT. Toulorge, W. Desmet. Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations Applied to Wave Propagation Problems. Journal of Computational Physics, 231(4), pp 2067-2091, 2012. doi: https://doi.org/10.1016/j.jcp.2011.11.024\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.DGLDDRK84_C","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.DGLDDRK84_C","text":"DGLDDRK84_C(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. 8-stage, fourth order low-storage low-dissipation, low-dispersion scheme for discontinuous Galerkin space discretizations applied to wave propagation problems. Optimized for PDE discretizations when maximum spatial step is small due to geometric features of computational domain. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nT. Toulorge, W. Desmet. Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations Applied to Wave Propagation Problems. Journal of Computational Physics, 231(4), pp 2067-2091, 2012. doi: https://doi.org/10.1016/j.jcp.2011.11.024\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.DGLDDRK84_F","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.DGLDDRK84_F","text":"DGLDDRK84_F(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. 8-stage, fourth order low-storage low-dissipation, low-dispersion scheme for discontinuous Galerkin space discretizations applied to wave propagation problems. Optimized for PDE discretizations when the maximum spatial step size is not constrained. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nT. Toulorge, W. Desmet. Optimal Runge–Kutta Schemes for Discontinuous Galerkin Space Discretizations Applied to Wave Propagation Problems. Journal of Computational Physics, 231(4), pp 2067-2091, 2012. doi: https://doi.org/10.1016/j.jcp.2011.11.024\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.NDBLSRK124","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.NDBLSRK124","text":"NDBLSRK124(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. 12-stage, fourth order low-storage method with optimized stability regions for advection-dominated problems. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nJens Niegemann, Richard Diehl, Kurt Busch. Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. Journal of Computational Physics, 231, pp 364-372, 2012. doi: https://doi.org/10.1016/j.jcp.2011.09.003\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.NDBLSRK134","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.NDBLSRK134","text":"NDBLSRK134(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. 13-stage, fourth order low-storage method with optimized stability regions for advection-dominated problems. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nJens Niegemann, Richard Diehl, Kurt Busch. Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. Journal of Computational Physics, 231, pp 364-372, 2012. doi: https://doi.org/10.1016/j.jcp.2011.09.003\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.NDBLSRK144","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.NDBLSRK144","text":"NDBLSRK144(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),\n williamson_condition = true)\n\nExplicit Runge-Kutta Method. 14-stage, fourth order low-storage method with optimized stability regions for advection-dominated problems. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\nwilliamson_condition: allows for an optimization that allows fusing broadcast expressions with the function call f. However, it only works for Array types.\n\nReferences\n\nJens Niegemann, Richard Diehl, Kurt Busch. Efficient Low-Storage Runge–Kutta Schemes with Optimized Stability Regions. Journal of Computational Physics, 231, pp 364-372, 2012. doi: https://doi.org/10.1016/j.jcp.2011.09.003\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CFRLDDRK64","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CFRLDDRK64","text":"CFRLDDRK64(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 6-stage, fourth order low-storage, low-dissipation, low-dispersion scheme. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nM. Calvo, J. M. Franco, L. Randez. A New Minimum Storage Runge–Kutta Scheme for Computational Acoustics. Journal of Computational Physics, 201, pp 1-12, 2004. doi: https://doi.org/10.1016/j.jcp.2004.05.012\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.TSLDDRK74","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.TSLDDRK74","text":"TSLDDRK74(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 7-stage, fourth order low-storage low-dissipation, low-dispersion scheme with maximal accuracy and stability limit along the imaginary axes. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nKostas Tselios, T. E. Simos. Optimized Runge–Kutta Methods with Minimal Dispersion and Dissipation for Problems arising from Computational Acoustics. Physics Letters A, 393(1-2), pp 38-47, 2007. doi: https://doi.org/10.1016/j.physleta.2006.10.072\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK43_2","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK43_2","text":"CKLLSRK43_2(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 4-stage, third order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK54_3C","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK54_3C","text":"CKLLSRK54_3C(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK95_4S","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK95_4S","text":"CKLLSRK95_4S(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK95_4C","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK95_4C","text":"CKLLSRK95_4C(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK95_4M","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK95_4M","text":"CKLLSRK95_4M(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 9-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK54_3C_3R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK54_3C_3R","text":"CKLLSRK54_3C_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK54_3M_3R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK54_3M_3R","text":"CKLLSRK54_3M_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK54_3N_3R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK54_3N_3R","text":"CKLLSRK54_3N_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK85_4C_3R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK85_4C_3R","text":"CKLLSRK85_4C_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK85_4M_3R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK85_4M_3R","text":"CKLLSRK85_4M_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK85_4P_3R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK85_4P_3R","text":"CKLLSRK85_4P_3R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK54_3N_4R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK54_3N_4R","text":"CKLLSRK54_3N_4R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK54_3M_4R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK54_3M_4R","text":"CKLLSRK54_3M_4R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 5-stage, fourth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK65_4M_4R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK65_4M_4R","text":"CKLLSRK65_4M_4R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. 6-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK85_4FM_4R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK85_4FM_4R","text":"CKLLSRK85_4FM_4R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 8-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.CKLLSRK75_4M_5R","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.CKLLSRK75_4M_5R","text":"CKLLSRK75_4M_5R(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. CKLLSRK754M5R: Low-Storage Method 7-stage, fifth order low-storage scheme, optimized for compressible Navier–Stokes equations.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.ParsaniKetchesonDeconinck3S32","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ParsaniKetchesonDeconinck3S32","text":"ParsaniKetchesonDeconinck3S32(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 3-stage, second order (3S) low-storage scheme, optimized the spectral difference method applied to wave propagation problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nParsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.ParsaniKetchesonDeconinck3S82","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ParsaniKetchesonDeconinck3S82","text":"ParsaniKetchesonDeconinck3S82(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 8-stage, second order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nParsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.ParsaniKetchesonDeconinck3S53","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ParsaniKetchesonDeconinck3S53","text":"ParsaniKetchesonDeconinck3S53(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 5-stage, third order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nParsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.ParsaniKetchesonDeconinck3S173","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ParsaniKetchesonDeconinck3S173","text":"ParsaniKetchesonDeconinck3S173(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 17-stage, third order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nParsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.ParsaniKetchesonDeconinck3S94","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ParsaniKetchesonDeconinck3S94","text":"ParsaniKetchesonDeconinck3S94(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 9-stage, fourth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nParsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.ParsaniKetchesonDeconinck3S184","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ParsaniKetchesonDeconinck3S184","text":"ParsaniKetchesonDeconinck3S184(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 18-stage, fourth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nParsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.ParsaniKetchesonDeconinck3S105","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ParsaniKetchesonDeconinck3S105","text":"ParsaniKetchesonDeconinck3S105(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 10-stage, fifth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nParsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.ParsaniKetchesonDeconinck3S205","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.ParsaniKetchesonDeconinck3S205","text":"ParsaniKetchesonDeconinck3S205(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. Low-Storage Method 20-stage, fifth order (3S) low-storage scheme, optimized for the spectral difference method applied to wave propagation problems.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nParsani, Matteo, David I. Ketcheson, and W. Deconinck. Optimized explicit Runge–Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM Journal on Scientific Computing 35.2 (2013): A957-A986. doi: https://doi.org/10.1137/120885899\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.RDPK3Sp35","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RDPK3Sp35","text":"RDPK3Sp35(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, five-stage explicit Runge-Kutta method with embedded error estimator designed for spectral element discretizations of compressible fluid mechanics.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRanocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.RDPK3SpFSAL35","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RDPK3SpFSAL35","text":"RDPK3SpFSAL35(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, five-stage explicit Runge-Kutta method with embedded error estimator using the FSAL property designed for spectral element discretizations of compressible fluid mechanics.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRanocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.RDPK3Sp49","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RDPK3Sp49","text":"RDPK3Sp49(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A fourth-order, nine-stage explicit Runge-Kutta method with embedded error estimator designed for spectral element discretizations of compressible fluid mechanics.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRanocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.RDPK3SpFSAL49","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RDPK3SpFSAL49","text":"RDPK3SpFSAL49(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A fourth-order, nine-stage explicit Runge-Kutta method with embedded error estimator using the FSAL property designed for spectral element discretizations of compressible fluid mechanics.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRanocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.RDPK3Sp510","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RDPK3Sp510","text":"RDPK3Sp510(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A fifth-order, ten-stage explicit Runge-Kutta method with embedded error estimator designed for spectral element discretizations of compressible fluid mechanics.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRanocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.RDPK3SpFSAL510","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.RDPK3SpFSAL510","text":"RDPK3SpFSAL510(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A fifth-order, ten-stage explicit Runge-Kutta method with embedded error estimator using the FSAL property designed for spectral element discretizations of compressible fluid mechanics.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRanocha, Dalcin, Parsani, Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#SSP-Optimized-Runge-Kutta-Methods","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"SSP Optimized Runge-Kutta Methods","text":"","category":"section"},{"location":"nonstiff/lowstorage_ssprk/","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"PDE-Specialized Explicit Runge-Kutta Methods","text":"KYK2014DGSSPRK_3S2\r\nSSPRK22\r\nSSPRK33\r\nSSPRK53\r\nKYKSSPRK42\r\nSSPRK53_2N1\r\nSSPRK53_2N2\r\nSSPRK53_H\r\nSSPRK63\r\nSSPRK73\r\nSSPRK83\r\nSSPRK43\r\nSSPRK432\r\nSSPRKMSVS43\r\nSSPRKMSVS32\r\nSSPRK932\r\nSSPRK54\r\nSSPRK104","category":"page"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.KYK2014DGSSPRK_3S2","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.KYK2014DGSSPRK_3S2","text":"KYK2014DGSSPRK_3S2(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. TBD\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK22","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK22","text":"SSPRK22(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A second-order, two-stage explicit strong stability preserving (SSP) method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nShu, Chi-Wang, and Stanley Osher. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics 77.2 (1988): 439-471. https://doi.org/10.1016/0021-9991(88)90177-5\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK33","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK33","text":"SSPRK33(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, three-stage explicit strong stability preserving (SSP) method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nShu, Chi-Wang, and Stanley Osher. Efficient implementation of essentially non-oscillatory shock-capturing schemes. Journal of Computational Physics 77.2 (1988): 439-471. https://doi.org/10.1016/0021-9991(88)90177-5\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK53","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK53","text":"SSPRK53(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, five-stage explicit strong stability preserving (SSP) method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRuuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.KYKSSPRK42","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.KYKSSPRK42","text":"KYKSSPRK42(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. TBD\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK53_2N1","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK53_2N1","text":"SSPRK53_2N1(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nHigueras and T. Roldán. New third order low-storage SSP explicit Runge–Kutta methods arXiv:1809.04807v1.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK53_2N2","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK53_2N2","text":"SSPRK53_2N2(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nHigueras and T. Roldán. New third order low-storage SSP explicit Runge–Kutta methods arXiv:1809.04807v1.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK53_H","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK53_H","text":"SSPRK53_H(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, five-stage explicit strong stability preserving (SSP) low-storage method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nHigueras and T. Roldán. New third order low-storage SSP explicit Runge–Kutta methods arXiv:1809.04807v1.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK63","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK63","text":"SSPRK63(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, six-stage explicit strong stability preserving (SSP) method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRuuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK73","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK73","text":"SSPRK73(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, seven-stage explicit strong stability preserving (SSP) method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRuuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK83","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK83","text":"SSPRK83(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, eight-stage explicit strong stability preserving (SSP) method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRuuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK43","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK43","text":"SSPRK43(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, four-stage explicit strong stability preserving (SSP) method.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nOptimal third-order explicit SSP method with four stages discovered by\n\nJ. F. B. M. Kraaijevanger. \"Contractivity of Runge-Kutta methods.\" In: BIT Numerical Mathematics 31.3 (1991), pp. 482–528. DOI: 10.1007/BF01933264.\n\nEmbedded method constructed by\n\nSidafa Conde, Imre Fekete, John N. Shadid. \"Embedded error estimation and adaptive step-size control for optimal explicit strong stability preserving Runge–Kutta methods.\" arXiv: 1806.08693\n\nEfficient implementation (and optimized controller) developed by\n\nHendrik Ranocha, Lisandro Dalcin, Matteo Parsani, David I. Ketcheson (2021) Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics arXiv:2104.06836\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK432","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK432","text":"SSPRK432(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, four-stage explicit strong stability preserving (SSP) method.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nGottlieb, Sigal, David I. Ketcheson, and Chi-Wang Shu. Strong stability preserving Runge-Kutta and multistep time discretizations. World Scientific, 2011. Example 6.1\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRKMSVS43","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRKMSVS43","text":"SSPRKMSVS43(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, four-step explicit strong stability preserving (SSP) linear multistep method. This method does not come with an error estimator and requires a fixed time step size.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nShu, Chi-Wang. Total-variation-diminishing time discretizations. SIAM Journal on Scientific and Statistical Computing 9, no. 6 (1988): 1073-1084. DOI: 10.1137/0909073\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRKMSVS32","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRKMSVS32","text":"SSPRKMSVS32(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A second-order, three-step explicit strong stability preserving (SSP) linear multistep method. This method does not come with an error estimator and requires a fixed time step size.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nShu, Chi-Wang. Total-variation-diminishing time discretizations. SIAM Journal on Scientific and Statistical Computing 9, no. 6 (1988): 1073-1084. DOI: 10.1137/0909073\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK932","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK932","text":"SSPRK932(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A third-order, nine-stage explicit strong stability preserving (SSP) method.\n\nConsider using SSPRK43 instead, which uses the same main method and an improved embedded method.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nGottlieb, Sigal, David I. Ketcheson, and Chi-Wang Shu. Strong stability preserving Runge-Kutta and multistep time discretizations. World Scientific, 2011.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK54","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK54","text":"SSPRK54(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A fourth-order, five-stage explicit strong stability preserving (SSP) method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nRuuth, Steven. Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Mathematics of Computation 75.253 (2006): 183-207.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/lowstorage_ssprk/#OrdinaryDiffEq.SSPRK104","page":"PDE-Specialized Explicit Runge-Kutta Methods","title":"OrdinaryDiffEq.SSPRK104","text":"SSPRK104(; stage_limiter! = OrdinaryDiffEq.trivial_limiter!,\n step_limiter! = OrdinaryDiffEq.trivial_limiter!,\n thread = OrdinaryDiffEq.False(),)\n\nExplicit Runge-Kutta Method. A fourth-order, ten-stage explicit strong stability preserving (SSP) method. Fixed timestep only.\n\nKeyword Arguments\n\nstage_limiter!: function of the form limiter!(u, integrator, p, t)\nstep_limiter!: function of the form limiter!(u, integrator, p, t)\nthread: determines whether internal broadcasting on appropriate CPU arrays should be serial (thread = OrdinaryDiffEq.False(), default) or use multiple threads (thread = OrdinaryDiffEq.True()) when Julia is started with multiple threads.\n\nReferences\n\nKetcheson, David I. Highly efficient strong stability-preserving Runge–Kutta methods with low-storage implementations. SIAM Journal on Scientific Computing 30.4 (2008): 2113-2136.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#Multistep-Methods-for-Non-Stiff-Equations","page":"Multistep Methods for Non-Stiff Equations","title":"Multistep Methods for Non-Stiff Equations","text":"","category":"section"},{"location":"nonstiff/nonstiff_multistep/#Explicit-Multistep-Methods","page":"Multistep Methods for Non-Stiff Equations","title":"Explicit Multistep Methods","text":"","category":"section"},{"location":"nonstiff/nonstiff_multistep/","page":"Multistep Methods for Non-Stiff Equations","title":"Multistep Methods for Non-Stiff Equations","text":"AB3\r\nAB4\r\nAB5\r\nAN5","category":"page"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.AB3","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.AB3","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nAB3: Adams-Bashforth Explicit Method The 3-step third order multistep method. Ralston's Second Order Method is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.AB4","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.AB4","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nAB4: Adams-Bashforth Explicit Method The 4-step fourth order multistep method. Runge-Kutta method of order 4 is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.AB5","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.AB5","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nAB5: Adams-Bashforth Explicit Method The 3-step third order multistep method. Ralston's Second Order Method is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.AN5","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.AN5","text":"AN5: Adaptive step size Adams explicit Method An adaptive 5th order fixed-leading coefficient Adams method in Nordsieck form.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#Predictor-Corrector-Methods","page":"Multistep Methods for Non-Stiff Equations","title":"Predictor-Corrector Methods","text":"","category":"section"},{"location":"nonstiff/nonstiff_multistep/","page":"Multistep Methods for Non-Stiff Equations","title":"Multistep Methods for Non-Stiff Equations","text":"ABM32\r\nABM43\r\nABM54\r\nVCAB3\r\nVCAB4\r\nVCAB5\r\nVCABM3\r\nVCABM4\r\nVCABM5\r\nVCABM\r\n","category":"page"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.ABM32","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.ABM32","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nABM32: Adams-Bashforth Explicit Method It is third order method. In ABM32, AB3 works as predictor and Adams Moulton 2-steps method works as Corrector. Ralston's Second Order Method is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.ABM43","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.ABM43","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nABM43: Adams-Bashforth Explicit Method It is fourth order method. In ABM43, AB4 works as predictor and Adams Moulton 3-steps method works as Corrector. Runge-Kutta method of order 4 is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.ABM54","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.ABM54","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nABM54: Adams-Bashforth Explicit Method It is fifth order method. In ABM54, AB5 works as predictor and Adams Moulton 4-steps method works as Corrector. Runge-Kutta method of order 4 is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.VCAB3","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.VCAB3","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nVCAB3: Adaptive step size Adams explicit Method The 3rd order Adams method. Bogacki-Shampine 3/2 method is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.VCAB4","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.VCAB4","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nVCAB4: Adaptive step size Adams explicit Method The 4th order Adams method. Runge-Kutta 4 is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.VCAB5","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.VCAB5","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nVCAB5: Adaptive step size Adams explicit Method The 5th order Adams method. Runge-Kutta 4 is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.VCABM3","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.VCABM3","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nVCABM3: Adaptive step size Adams explicit Method The 3rd order Adams-Moulton method. Bogacki-Shampine 3/2 method is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.VCABM4","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.VCABM4","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nVCABM4: Adaptive step size Adams explicit Method The 4th order Adams-Moulton method. Runge-Kutta 4 is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.VCABM5","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.VCABM5","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nVCABM5: Adaptive step size Adams explicit Method The 5th order Adams-Moulton method. Runge-Kutta 4 is used to calculate starting values.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/nonstiff_multistep/#OrdinaryDiffEq.VCABM","page":"Multistep Methods for Non-Stiff Equations","title":"OrdinaryDiffEq.VCABM","text":"E. Hairer, S. P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems. Computational Mathematics (2nd revised ed.), Springer (1996) doi: https://doi.org/10.1007/978-3-540-78862-1\n\nVCABM: Adaptive step size Adams explicit Method An adaptive order adaptive time Adams Moulton method. It uses an order adaptivity algorithm is derived from Shampine's DDEABM.\n\n\n\n\n\n","category":"type"},{"location":"stiff/rosenbrock/#Rosenbrock-Methods","page":"Rosenbrock Methods","title":"Rosenbrock Methods","text":"","category":"section"},{"location":"stiff/rosenbrock/#Standard-Rosenbrock-Methods","page":"Rosenbrock Methods","title":"Standard Rosenbrock Methods","text":"","category":"section"},{"location":"stiff/rosenbrock/","page":"Rosenbrock Methods","title":"Rosenbrock Methods","text":"ROS3P\r\nRodas3\r\nRosShamp4\r\nVeldd4\r\nVelds4\r\nGRK4T\r\nGRK4A\r\nRos4LStab\r\nRodas4\r\nRodas42\r\nRodas4P\r\nRodas4P2\r\nRodas5\r\nRodas5P\r\nGeneralRosenbrock","category":"page"},{"location":"stiff/rosenbrock/#Rosenbrock-W-Methods","page":"Rosenbrock Methods","title":"Rosenbrock W-Methods","text":"","category":"section"},{"location":"stiff/rosenbrock/","page":"Rosenbrock Methods","title":"Rosenbrock Methods","text":"Rosenbrock23\r\nRosenbrock32\r\nROS34PW1a\r\nROS34PW1b\r\nROS34PW2\r\nROS34PW3\r\nRosenbrockW6S4OS","category":"page"},{"location":"stiff/rosenbrock/#OrdinaryDiffEq.RosenbrockW6S4OS","page":"Rosenbrock Methods","title":"OrdinaryDiffEq.RosenbrockW6S4OS","text":"RosenbrockW6S4OS: Rosenbrock-W Method A 4th order L-stable Rosenbrock-W method (fixed step only).\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#Symplectic-Runge-Kutta-Methods","page":"Symplectic Runge-Kutta Methods","title":"Symplectic Runge-Kutta Methods","text":"","category":"section"},{"location":"dynamical/symplectic/","page":"Symplectic Runge-Kutta Methods","title":"Symplectic Runge-Kutta Methods","text":"SymplecticEuler\r\nVelocityVerlet\r\nVerletLeapfrog\r\nPseudoVerletLeapfrog\r\nMcAte2\r\nRuth3\r\nMcAte3\r\nCandyRoz4\r\nMcAte4\r\nCalvoSanz4\r\nMcAte42\r\nMcAte5\r\nYoshida6\r\nKahanLi6\r\nMcAte8\r\nKahanLi8\r\nSofSpa10","category":"page"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.VelocityVerlet","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.VelocityVerlet","text":"@article{verlet1967computer, title={Computer\" experiments\" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules}, author={Verlet, Loup}, journal={Physical review}, volume={159}, number={1}, pages={98}, year={1967}, publisher={APS} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.VerletLeapfrog","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.VerletLeapfrog","text":"@article{verlet1967computer, title={Computer\" experiments\" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules}, author={Verlet, Loup}, journal={Physical review}, volume={159}, number={1}, pages={98}, year={1967}, publisher={APS} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.PseudoVerletLeapfrog","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.PseudoVerletLeapfrog","text":"@article{verlet1967computer, title={Computer\" experiments\" on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules}, author={Verlet, Loup}, journal={Physical review}, volume={159}, number={1}, pages={98}, year={1967}, publisher={APS} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.McAte2","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.McAte2","text":"@article{mclachlan1992accuracy, title={The accuracy of symplectic integrators}, author={McLachlan, Robert I and Atela, Pau}, journal={Nonlinearity}, volume={5}, number={2}, pages={541}, year={1992}, publisher={IOP Publishing} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.Ruth3","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.Ruth3","text":"@article{ruth1983canonical, title={A canonical integration technique}, author={Ruth, Ronald D}, journal={IEEE Trans. Nucl. Sci.}, volume={30}, number={CERN-LEP-TH-83-14}, pages={2669–2671}, year={1983} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.McAte3","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.McAte3","text":"@article{mclachlan1992accuracy, title={The accuracy of symplectic integrators}, author={McLachlan, Robert I and Atela, Pau}, journal={Nonlinearity}, volume={5}, number={2}, pages={541}, year={1992}, publisher={IOP Publishing} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.CandyRoz4","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.CandyRoz4","text":"@article{candy1991symplectic, title={A symplectic integration algorithm for separable Hamiltonian functions}, author={Candy, J and Rozmus, W}, journal={Journal of Computational Physics}, volume={92}, number={1}, pages={230–256}, year={1991}, publisher={Elsevier} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.CalvoSanz4","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.CalvoSanz4","text":"@article{sanz1993symplectic, title={Symplectic numerical methods for Hamiltonian problems}, author={Sanz-Serna, Jes{'u}s Maria and Calvo, Mari-Paz}, journal={International Journal of Modern Physics C}, volume={4}, number={02}, pages={385–392}, year={1993}, publisher={World Scientific} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.McAte42","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.McAte42","text":"@article{mclachlan1992accuracy, title={The accuracy of symplectic integrators}, author={McLachlan, Robert I and Atela, Pau}, journal={Nonlinearity}, volume={5}, number={2}, pages={541}, year={1992}, publisher={IOP Publishing} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.McAte5","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.McAte5","text":"@article{mclachlan1992accuracy, title={The accuracy of symplectic integrators}, author={McLachlan, Robert I and Atela, Pau}, journal={Nonlinearity}, volume={5}, number={2}, pages={541}, year={1992}, publisher={IOP Publishing} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.Yoshida6","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.Yoshida6","text":"@article{yoshida1990construction, title={Construction of higher order symplectic integrators}, author={Yoshida, Haruo}, journal={Physics letters A}, volume={150}, number={5-7}, pages={262–268}, year={1990}, publisher={Elsevier} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.KahanLi6","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.KahanLi6","text":"@article{kahan1997composition, title={Composition constants for raising the orders of unconventional schemes for ordinary differential equations}, author={Kahan, William and Li, Ren-Cang}, journal={Mathematics of computation}, volume={66}, number={219}, pages={1089–1099}, year={1997} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.McAte8","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.McAte8","text":"@article{mclachlan1995numerical, title={On the numerical integration of ordinary differential equations by symmetric composition methods}, author={McLachlan, Robert I}, journal={SIAM Journal on Scientific Computing}, volume={16}, number={1}, pages={151–168}, year={1995}, publisher={SIAM} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.KahanLi8","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.KahanLi8","text":"@article{kahan1997composition, title={Composition constants for raising the orders of unconventional schemes for ordinary differential equations}, author={Kahan, William and Li, Ren-Cang}, journal={Mathematics of computation}, volume={66}, number={219}, pages={1089–1099}, year={1997} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/symplectic/#OrdinaryDiffEq.SofSpa10","page":"Symplectic Runge-Kutta Methods","title":"OrdinaryDiffEq.SofSpa10","text":"@article{sofroniou2005derivation, title={Derivation of symmetric composition constants for symmetric integrators}, author={Sofroniou, Mark and Spaletta, Giulia}, journal={Optimization Methods and Software}, volume={20}, number={4-5}, pages={597–613}, year={2005}, publisher={Taylor \\& Francis} }\n\n\n\n\n\n","category":"type"},{"location":"misc/","page":"-","title":"-","text":"LinearExponential\r\nSplitEuler\r\nCompositeAlgorithm\r\nPDIRK44","category":"page"},{"location":"misc/#OrdinaryDiffEq.PDIRK44","page":"-","title":"OrdinaryDiffEq.PDIRK44","text":"PDIRK44: Parallel Diagonally Implicit Runge-Kutta Method A 2 processor 4th order diagonally non-adaptive implicit method.\n\n\n\n\n\n","category":"type"},{"location":"stiff/firk/#Fully-Implicit-Runge-Kutta-(FIRK)-Methods","page":"Fully Implicit Runge-Kutta (FIRK) Methods","title":"Fully Implicit Runge-Kutta (FIRK) Methods","text":"","category":"section"},{"location":"stiff/firk/","page":"Fully Implicit Runge-Kutta (FIRK) Methods","title":"Fully Implicit Runge-Kutta (FIRK) Methods","text":"RadauIIA3\r\nRadauIIA5","category":"page"},{"location":"stiff/firk/#OrdinaryDiffEq.RadauIIA3","page":"Fully Implicit Runge-Kutta (FIRK) Methods","title":"OrdinaryDiffEq.RadauIIA3","text":"@article{hairer1999stiff, title={Stiff differential equations solved by Radau methods}, author={Hairer, Ernst and Wanner, Gerhard}, journal={Journal of Computational and Applied Mathematics}, volume={111}, number={1-2}, pages={93–111}, year={1999}, publisher={Elsevier} }\n\nRadauIIA3: Fully-Implicit Runge-Kutta Method An A-B-L stable fully implicit Runge-Kutta method with internal tableau complex basis transform for efficiency.\n\n\n\n\n\n","category":"type"},{"location":"stiff/firk/#OrdinaryDiffEq.RadauIIA5","page":"Fully Implicit Runge-Kutta (FIRK) Methods","title":"OrdinaryDiffEq.RadauIIA5","text":"@article{hairer1999stiff, title={Stiff differential equations solved by Radau methods}, author={Hairer, Ernst and Wanner, Gerhard}, journal={Journal of Computational and Applied Mathematics}, volume={111}, number={1-2}, pages={93–111}, year={1999}, publisher={Elsevier} }\n\nRadauIIA5: Fully-Implicit Runge-Kutta Method An A-B-L stable fully implicit Runge-Kutta method with internal tableau complex basis transform for efficiency.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicit_extrapolation/#Explicit-Extrapolation-Methods","page":"Explicit Extrapolation Methods","title":"Explicit Extrapolation Methods","text":"","category":"section"},{"location":"nonstiff/explicit_extrapolation/","page":"Explicit Extrapolation Methods","title":"Explicit Extrapolation Methods","text":"AitkenNeville\r\nExtrapolationMidpointDeuflhard\r\nExtrapolationMidpointHairerWanner","category":"page"},{"location":"nonstiff/explicit_extrapolation/#OrdinaryDiffEq.AitkenNeville","page":"Explicit Extrapolation Methods","title":"OrdinaryDiffEq.AitkenNeville","text":"AitkenNeville: Parallelized Explicit Extrapolation Method Euler extrapolation using Aitken-Neville with the Romberg Sequence.\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicit_extrapolation/#OrdinaryDiffEq.ExtrapolationMidpointDeuflhard","page":"Explicit Extrapolation Methods","title":"OrdinaryDiffEq.ExtrapolationMidpointDeuflhard","text":"ExtrapolationMidpointDeuflhard: Parallelized Explicit Extrapolation Method Midpoint extrapolation using Barycentric coordinates\n\n\n\n\n\n","category":"type"},{"location":"nonstiff/explicit_extrapolation/#OrdinaryDiffEq.ExtrapolationMidpointHairerWanner","page":"Explicit Extrapolation Methods","title":"OrdinaryDiffEq.ExtrapolationMidpointHairerWanner","text":"ExtrapolationMidpointHairerWanner: Parallelized Explicit Extrapolation Method Midpoint extrapolation using Barycentric coordinates, following Hairer's ODEX in the adaptivity behavior.\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_multistep/#IMEX-Multistep-Methods","page":"IMEX Multistep Methods","title":"IMEX Multistep Methods","text":"","category":"section"},{"location":"imex/imex_multistep/","page":"IMEX Multistep Methods","title":"IMEX Multistep Methods","text":"CNAB2\r\nCNLF2\r\nSBDF\r\nSBDF2\r\nSBDF3\r\nSBDF4","category":"page"},{"location":"imex/imex_multistep/#OrdinaryDiffEq.SBDF2","page":"IMEX Multistep Methods","title":"OrdinaryDiffEq.SBDF2","text":"SBDF2(;kwargs...)\n\nThe two-step version of the IMEX multistep methods of\n\nUri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037\n\nSee also SBDF.\n\n\n\n\n\n","category":"function"},{"location":"imex/imex_multistep/#OrdinaryDiffEq.SBDF3","page":"IMEX Multistep Methods","title":"OrdinaryDiffEq.SBDF3","text":"SBDF3(;kwargs...)\n\nThe three-step version of the IMEX multistep methods of\n\nUri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037\n\nSee also SBDF.\n\n\n\n\n\n","category":"function"},{"location":"imex/imex_multistep/#OrdinaryDiffEq.SBDF4","page":"IMEX Multistep Methods","title":"OrdinaryDiffEq.SBDF4","text":"SBDF4(;kwargs...)\n\nThe four-step version of the IMEX multistep methods of\n\nUri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037\n\nSee also SBDF.\n\n\n\n\n\n","category":"function"},{"location":"semilinear/exponential_rk/#Exponential-Runge-Kutta-Integrators","page":"Exponential Runge-Kutta Integrators","title":"Exponential Runge-Kutta Integrators","text":"","category":"section"},{"location":"semilinear/exponential_rk/","page":"Exponential Runge-Kutta Integrators","title":"Exponential Runge-Kutta Integrators","text":"LawsonEuler\r\nNorsettEuler\r\nETD2\r\nETDRK2\r\nETDRK3\r\nETDRK4\r\nHochOst4\r\nExp4\r\nEPIRK4s3A\r\nEPIRK4s3B\r\nEPIRK5s3\r\nEXPRB53s3\r\nEPIRK5P1\r\nEPIRK5P2","category":"page"},{"location":"semilinear/exponential_rk/#OrdinaryDiffEq.ETD2","page":"Exponential Runge-Kutta Integrators","title":"OrdinaryDiffEq.ETD2","text":"ETD2: Exponential Runge-Kutta Method Second order Exponential Time Differencing method (in development).\n\n\n\n\n\n","category":"type"},{"location":"usage/#Usage","page":"Usage","title":"Usage","text":"","category":"section"},{"location":"usage/","page":"Usage","title":"Usage","text":"OrdinaryDiffEq.jl is part of the SciML common interface, but can be used independently of DifferentialEquations.jl. The only requirement is that the user passes an OrdinaryDiffEq.jl algorithm to solve. For example, we can solve the ODE tutorial from the docs using the Tsit5() algorithm:","category":"page"},{"location":"usage/","page":"Usage","title":"Usage","text":"using OrdinaryDiffEq\nf(u,p,t) = 1.01*u\nu0=1/2\ntspan = (0.0,1.0)\nprob = ODEProblem(f,u0,tspan)\nsol = solve(prob,Tsit5(),reltol=1e-8,abstol=1e-8)\nusing Plots\nplot(sol,linewidth=5,title=\"Solution to the linear ODE with a thick line\",\n xaxis=\"Time (t)\",yaxis=\"u(t) (in μm)\",label=\"My Thick Line!\") # legend=false\nplot!(sol.t, t->0.5*exp(1.01t),lw=3,ls=:dash,label=\"True Solution!\")","category":"page"},{"location":"usage/","page":"Usage","title":"Usage","text":"That example uses the out-of-place syntax f(u,p,t), while the inplace syntax (more efficient for systems of equations) is shown in the Lorenz example:","category":"page"},{"location":"usage/","page":"Usage","title":"Usage","text":"using OrdinaryDiffEq\nfunction lorenz(du,u,p,t)\n du[1] = 10.0(u[2]-u[1])\n du[2] = u[1]*(28.0-u[3]) - u[2]\n du[3] = u[1]*u[2] - (8/3)*u[3]\nend\nu0 = [1.0;0.0;0.0]\ntspan = (0.0,100.0)\nprob = ODEProblem(lorenz,u0,tspan)\nsol = solve(prob,Tsit5())\nusing Plots; plot(sol,vars=(1,2,3))","category":"page"},{"location":"usage/","page":"Usage","title":"Usage","text":"Very fast static array versions can be specifically compiled to the size of your model. For example:","category":"page"},{"location":"usage/","page":"Usage","title":"Usage","text":"using OrdinaryDiffEq, StaticArrays\nfunction lorenz(u,p,t)\n SA[10.0(u[2]-u[1]),u[1]*(28.0-u[3]) - u[2],u[1]*u[2] - (8/3)*u[3]]\nend\nu0 = SA[1.0;0.0;0.0]\ntspan = (0.0,100.0)\nprob = ODEProblem(lorenz,u0,tspan)\nsol = solve(prob,Tsit5())","category":"page"},{"location":"usage/","page":"Usage","title":"Usage","text":"For “refined ODEs”, like dynamical equations and SecondOrderODEProblems, refer to the DiffEqDocs. For example, in DiffEqTutorials.jl we show how to solve equations of motion using symplectic methods:","category":"page"},{"location":"usage/","page":"Usage","title":"Usage","text":"function HH_acceleration(dv,v,u,p,t)\n x,y = u\n dx,dy = dv\n dv[1] = -x - 2x*y\n dv[2] = y^2 - y -x^2\nend\ninitial_positions = [0.0,0.1]\ninitial_velocities = [0.5,0.0]\nprob = SecondOrderODEProblem(HH_acceleration,initial_velocities,initial_positions,tspan)\nsol2 = solve(prob, KahanLi8(), dt=1/10);","category":"page"},{"location":"usage/","page":"Usage","title":"Usage","text":"Other refined forms are IMEX and semi-linear ODEs (for exponential integrators).","category":"page"},{"location":"usage/#Available-Solvers","page":"Usage","title":"Available Solvers","text":"","category":"section"},{"location":"usage/","page":"Usage","title":"Usage","text":"For the list of available solvers, please refer to the DifferentialEquations.jl ODE Solvers, Dynamical ODE Solvers, and the Split ODE Solvers pages.","category":"page"},{"location":"stiff/stabilized_rk/#Stabilized-Runge-Kutta-Methods-(Runge-Kutta-Chebyshev)","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","text":"","category":"section"},{"location":"stiff/stabilized_rk/#Explicit-Stabilized-Runge-Kutta-Methods","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"Explicit Stabilized Runge-Kutta Methods","text":"","category":"section"},{"location":"stiff/stabilized_rk/","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","text":"Explicit stabilized methods utilize an upper bound on the spectral radius of the Jacobian. Users can supply an upper bound by specifying the keyword argument eigen_est, for example","category":"page"},{"location":"stiff/stabilized_rk/","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","text":"`eigen_est = (integrator) -> integrator.eigen_est = upper_bound`","category":"page"},{"location":"stiff/stabilized_rk/","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","text":"The methods ROCK2 and ROCK4 also include keyword arguments min_stages and max_stages, which specify upper and lower bounds on the adaptively chosen number of stages for stability. ","category":"page"},{"location":"stiff/stabilized_rk/","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","text":"ROCK2\r\nROCK4\r\nSERK2\r\nESERK4\r\nESERK5\r\nRKC","category":"page"},{"location":"stiff/stabilized_rk/#OrdinaryDiffEq.ROCK2","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"OrdinaryDiffEq.ROCK2","text":"Assyr Abdulle, Alexei A. Medovikov. Second Order Chebyshev Methods based on Orthogonal Polynomials. Numerische Mathematik, 90 (1), pp 1-18, 2001. doi: https://dx.doi.org/10.1007/s002110100292\n\nROCK2: Stabilized Explicit Method. Second order stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues and is smoothened to allow for moderate sized complex eigenvalues.\n\nThis method takes optional keyword arguments min_stages, max_stages, and eigen_est. The function eigen_est should be of the form\n\neigen_est = (integrator) -> integrator.eigen_est = upper_bound,\n\nwhere upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.\n\n\n\n\n\n","category":"type"},{"location":"stiff/stabilized_rk/#OrdinaryDiffEq.ROCK4","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"OrdinaryDiffEq.ROCK4","text":"ROCK4(; min_stages = 0, max_stages = 152, eigen_est = nothing)\n\nAssyr Abdulle. Fourth Order Chebyshev Methods With Recurrence Relation. 2002 Society for Industrial and Applied Mathematics Journal on Scientific Computing, 23(6), pp 2041-2054, 2001. doi: https://doi.org/10.1137/S1064827500379549\n\nROCK4: Stabilized Explicit Method. Fourth order stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues and is smoothened to allow for moderate sized complex eigenvalues.\n\nThis method takes optional keyword arguments min_stages, max_stages, and eigen_est. The function eigen_est should be of the form\n\neigen_est = (integrator) -> integrator.eigen_est = upper_bound,\n\nwhere upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.\n\n\n\n\n\n","category":"type"},{"location":"stiff/stabilized_rk/#OrdinaryDiffEq.ESERK4","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"OrdinaryDiffEq.ESERK4","text":"ESERK4(; eigen_est = nothing)\n\nJ. Martín-Vaquero, B. Kleefeld. Extrapolated stabilized explicit Runge-Kutta methods, Journal of Computational Physics, 326, pp 141-155, 2016. doi: https://doi.org/10.1016/j.jcp.2016.08.042.\n\nESERK4: Stabilized Explicit Method. Fourth order extrapolated stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues and is smoothened to allow for moderate sized complex eigenvalues.\n\nThis method takes the keyword argument eigen_est of the form\n\neigen_est = (integrator) -> integrator.eigen_est = upper_bound,\n\nwhere upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.\n\n\n\n\n\n","category":"type"},{"location":"stiff/stabilized_rk/#OrdinaryDiffEq.ESERK5","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"OrdinaryDiffEq.ESERK5","text":"ESERK5(; eigen_est = nothing)\n\nJ. Martín-Vaquero, A. Kleefeld. ESERK5: A fifth-order extrapolated stabilized explicit Runge-Kutta method, Journal of Computational and Applied Mathematics, 356, pp 22-36, 2019. doi: https://doi.org/10.1016/j.cam.2019.01.040.\n\nESERK5: Stabilized Explicit Method. Fifth order extrapolated stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues and is smoothened to allow for moderate sized complex eigenvalues.\n\nThis method takes the keyword argument eigen_est of the form\n\neigen_est = (integrator) -> integrator.eigen_est = upper_bound,\n\nwhere upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.\n\n\n\n\n\n","category":"type"},{"location":"stiff/stabilized_rk/#OrdinaryDiffEq.RKC","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"OrdinaryDiffEq.RKC","text":"RKC(; eigen_est = nothing)\n\nB. P. Sommeijer, L. F. Shampine, J. G. Verwer. RKC: An Explicit Solver for Parabolic PDEs, Journal of Computational and Applied Mathematics, 88(2), pp 315-326, 1998. doi: https://doi.org/10.1016/S0377-0427(97)00219-7\n\nRKC: Stabilized Explicit Method. Second order stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues.\n\nThis method takes the keyword argument eigen_est of the form\n\neigen_est = (integrator) -> integrator.eigen_est = upper_bound,\n\nwhere upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.\n\n\n\n\n\n","category":"type"},{"location":"stiff/stabilized_rk/#Implicit-Stabilized-Runge-Kutta-Methods","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"Implicit Stabilized Runge-Kutta Methods","text":"","category":"section"},{"location":"stiff/stabilized_rk/","page":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","title":"Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)","text":"IRKC","category":"page"},{"location":"dynamical/nystrom/#Runge-Kutta-Nystrom-Methods","page":"Runge-Kutta Nystrom Methods","title":"Runge-Kutta Nystrom Methods","text":"","category":"section"},{"location":"dynamical/nystrom/","page":"Runge-Kutta Nystrom Methods","title":"Runge-Kutta Nystrom Methods","text":"IRKN3\r\nIRKN4\r\nNystrom4\r\nNystrom4VelocityIndependent\r\nNystrom5VelocityIndependent\r\nFineRKN4\r\nFineRKN5\r\nDPRKN6\r\nDPRKN6FM\r\nDPRKN8\r\nDPRKN12\r\nERKN4\r\nERKN5\r\nERKN7","category":"page"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.IRKN3","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.IRKN3","text":"IRKN3\n\nImproved Runge-Kutta-Nyström method of order three, which minimizes the amount of evaluated functions in each step. Fixed time steps only.\n\nSecond order ODE should not depend on the first derivative.\n\nReferences\n\n@article{rabiei2012numerical, title={Numerical Solution of Second-Order Ordinary Differential Equations by Improved Runge-Kutta Nystrom Method}, author={Rabiei, Faranak and Ismail, Fudziah and Norazak, S and Emadi, Saeid}, publisher={Citeseer} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.IRKN4","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.IRKN4","text":"IRKN4\n\nImproves Runge-Kutta-Nyström method of order four, which minimizes the amount of evaluated functions in each step. Fixed time steps only.\n\nSecond order ODE should not be dependent on the first derivative.\n\nRecommended for smooth problems with expensive functions to evaluate.\n\nReferences\n\n@article{rabiei2012numerical, title={Numerical Solution of Second-Order Ordinary Differential Equations by Improved Runge-Kutta Nystrom Method}, author={Rabiei, Faranak and Ismail, Fudziah and Norazak, S and Emadi, Saeid}, publisher={Citeseer} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.Nystrom4","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.Nystrom4","text":"Nystrom4\n\nA 4th order explicit Runge-Kutta-Nyström method which can be applied directly on second order ODEs. Can only be used with fixed time steps.\n\nIn case the ODE Problem is not dependent on the first derivative consider using Nystrom4VelocityIndependent to increase performance.\n\nReferences\n\nE. Hairer, S.P. Norsett, G. Wanner, (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series in Computational Mathematics, Springer-Verlag.\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.Nystrom4VelocityIndependent","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.Nystrom4VelocityIndependent","text":"Nystrom4VelocityIdependent\n\nA 4th order explicit Runkge-Kutta-Nyström method. Used directly on second order ODEs, where the acceleration is independent from velocity (ODE Problem is not dependent on the first derivative).\n\nMore efficient then Nystrom4 on velocity independent problems, since less evaluations are needed.\n\nFixed time steps only.\n\nReferences\n\nE. Hairer, S.P. Norsett, G. Wanner, (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series in Computational Mathematics, Springer-Verlag.\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.Nystrom5VelocityIndependent","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.Nystrom5VelocityIndependent","text":"Nystrom5VelocityIndependent\n\nA 5th order explicit Runkge-Kutta-Nyström method. Used directly on second order ODEs, where the acceleration is independent from velocity (ODE Problem is not dependent on the first derivative). Fixed time steps only.\n\nReferences\n\nE. Hairer, S.P. Norsett, G. Wanner, (1993) Solving Ordinary Differential Equations I. Nonstiff Problems. 2nd Edition. Springer Series in Computational Mathematics, Springer-Verlag.\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.FineRKN4","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.FineRKN4","text":"FineRKN4()\n\nA 4th order explicit Runge-Kutta-Nyström method which can be applied directly to second order ODEs. In particular, this method allows the acceleration equation to depend on the velocity.\n\nReferences\n\n@article{fine1987low,\n title={Low order practical {R}unge-{K}utta-{N}ystr{\"o}m methods},\n author={Fine, Jerry Michael},\n journal={Computing},\n volume={38},\n number={4},\n pages={281--297},\n year={1987},\n publisher={Springer}\n}\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.FineRKN5","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.FineRKN5","text":"FineRKN5()\n\nA 5th order explicit Runge-Kutta-Nyström method which can be applied directly to second order ODEs. In particular, this method allows the acceleration equation to depend on the velocity.\n\nReferences\n\n@article{fine1987low,\n title={Low order practical {R}unge-{K}utta-{N}ystr{\"o}m methods},\n author={Fine, Jerry Michael},\n journal={Computing},\n volume={38},\n number={4},\n pages={281--297},\n year={1987},\n publisher={Springer}\n}\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.DPRKN6","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.DPRKN6","text":"DPRKN6\n\n6th order explicit Runge-Kutta-Nyström method. The second order ODE should not depend on the first derivative. Free 6th order interpolant.\n\nReferences\n\n@article{dormand1987runge, title={Runge-kutta-nystrom triples}, author={Dormand, JR and Prince, PJ}, journal={Computers \\& Mathematics with Applications}, volume={13}, number={12}, pages={937–949}, year={1987}, publisher={Elsevier} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.DPRKN6FM","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.DPRKN6FM","text":"DPRKN6FM\n\n6th order explicit Runge-Kutta-Nyström method. The second order ODE should not depend on the first derivative.\n\nCompared to DPRKN6, this method has smaller truncation error coefficients which leads to performance gain when only the main solution points are considered.\n\nReferences\n\n@article{Dormand1987FamiliesOR, title={Families of Runge-Kutta-Nystrom Formulae}, author={J. R. Dormand and Moawwad E. A. El-Mikkawy and P. J. Prince}, journal={Ima Journal of Numerical Analysis}, year={1987}, volume={7}, pages={235-250} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.DPRKN8","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.DPRKN8","text":"DPRKN8\n\n8th order explicit Runge-Kutta-Nyström method. The second order ODE should not depend on the first derivative.\n\nNot as efficient as DPRKN12 when high accuracy is needed, however this solver is competitive with DPRKN6 at lax tolerances and, depending on the problem, might be a good option between performance and accuracy.\n\nReferences\n\n@article{dormand1987high, title={High-order embedded Runge-Kutta-Nystrom formulae}, author={Dormand, JR and El-Mikkawy, MEA and Prince, PJ}, journal={IMA Journal of Numerical Analysis}, volume={7}, number={4}, pages={423–430}, year={1987}, publisher={Oxford University Press} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.DPRKN12","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.DPRKN12","text":"DPRKN12\n\n12th order explicit Rugne-Kutta-Nyström method. The second order ODE should not depend on the first derivative.\n\nMost efficient when high accuracy is needed.\n\nReferences\n\n@article{dormand1987high, title={High-order embedded Runge-Kutta-Nystrom formulae}, author={Dormand, JR and El-Mikkawy, MEA and Prince, PJ}, journal={IMA Journal of Numerical Analysis}, volume={7}, number={4}, pages={423–430}, year={1987}, publisher={Oxford University Press} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.ERKN4","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.ERKN4","text":"ERKN4\n\nEmbedded 4(3) pair of explicit Runge-Kutta-Nyström methods. Integrates the periodic properties of the harmonic oscillator exactly.\n\nThe second order ODE should not depend on the first derivative.\n\nUses adaptive step size control. This method is extra efficient on periodic problems.\n\nReferences\n\n@article{demba2017embedded, title={An Embedded 4 (3) Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nystr{\"o}m Method for Solving Periodic Initial Value Problems}, author={Demba, MA and Senu, N and Ismail, F}, journal={Applied Mathematical Sciences}, volume={11}, number={17}, pages={819–838}, year={2017} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.ERKN5","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.ERKN5","text":"ERKN5\n\nEmbedded 5(4) pair of explicit Runge-Kutta-Nyström methods. Integrates the periodic properties of the harmonic oscillator exactly.\n\nThe second order ODE should not depend on the first derivative.\n\nUses adaptive step size control. This method is extra efficient on periodic problems.\n\nReferences\n\n@article{demba20165, title={A 5 (4) Embedded Pair of Explicit Trigonometrically-Fitted Runge–Kutta–Nystr{\"o}m Methods for the Numerical Solution of Oscillatory Initial Value Problems}, author={Demba, Musa A and Senu, Norazak and Ismail, Fudziah}, journal={Mathematical and Computational Applications}, volume={21}, number={4}, pages={46}, year={2016}, publisher={Multidisciplinary Digital Publishing Institute} }\n\n\n\n\n\n","category":"type"},{"location":"dynamical/nystrom/#OrdinaryDiffEq.ERKN7","page":"Runge-Kutta Nystrom Methods","title":"OrdinaryDiffEq.ERKN7","text":"ERKN7\n\nEmbedded pair of explicit Runge-Kutta-Nyström methods. Integrates the periodic properties of the harmonic oscillator exactly.\n\nThe second order ODE should not depend on the first derivative.\n\nUses adaptive step size control. This method is extra efficient on periodic Problems.\n\nReferences\n\n@article{SimosOnHO, title={On high order Runge-Kutta-Nystr{\"o}m pairs}, author={Theodore E. Simos and Ch. Tsitouras}, journal={J. Comput. Appl. Math.}, volume={400}, pages={113753} }\n\n\n\n\n\n","category":"type"},{"location":"stiff/implicit_extrapolation/#Implicit-Extrapolation-Methods","page":"Implicit Extrapolation Methods","title":"Implicit Extrapolation Methods","text":"","category":"section"},{"location":"stiff/implicit_extrapolation/","page":"Implicit Extrapolation Methods","title":"Implicit Extrapolation Methods","text":"ImplicitEulerExtrapolation\r\nImplicitDeuflhardExtrapolation\r\nImplicitHairerWannerExtrapolation\r\nImplicitEulerBarycentricExtrapolation","category":"page"},{"location":"stiff/implicit_extrapolation/#OrdinaryDiffEq.ImplicitEulerExtrapolation","page":"Implicit Extrapolation Methods","title":"OrdinaryDiffEq.ImplicitEulerExtrapolation","text":"ImplicitEulerExtrapolation: Parallelized Implicit Extrapolation Method Extrapolation of implicit Euler method with Romberg sequence. Similar to Hairer's SEULEX.\n\n\n\n\n\n","category":"type"},{"location":"stiff/implicit_extrapolation/#OrdinaryDiffEq.ImplicitDeuflhardExtrapolation","page":"Implicit Extrapolation Methods","title":"OrdinaryDiffEq.ImplicitDeuflhardExtrapolation","text":"ImplicitDeuflhardExtrapolation: Parallelized Implicit Extrapolation Method Midpoint extrapolation using Barycentric coordinates\n\n\n\n\n\n","category":"type"},{"location":"stiff/implicit_extrapolation/#OrdinaryDiffEq.ImplicitHairerWannerExtrapolation","page":"Implicit Extrapolation Methods","title":"OrdinaryDiffEq.ImplicitHairerWannerExtrapolation","text":"ImplicitHairerWannerExtrapolation: Parallelized Implicit Extrapolation Method Midpoint extrapolation using Barycentric coordinates, following Hairer's SODEX in the adaptivity behavior.\n\n\n\n\n\n","category":"type"},{"location":"stiff/implicit_extrapolation/#OrdinaryDiffEq.ImplicitEulerBarycentricExtrapolation","page":"Implicit Extrapolation Methods","title":"OrdinaryDiffEq.ImplicitEulerBarycentricExtrapolation","text":"ImplicitEulerBarycentricExtrapolation: Parallelized Implicit Extrapolation Method Euler extrapolation using Barycentric coordinates, following Hairer's SODEX in the adaptivity behavior.\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#IMEX-SDIRK-Methods","page":"IMEX SDIRK Methods","title":"IMEX SDIRK Methods","text":"","category":"section"},{"location":"imex/imex_sdirk/","page":"IMEX SDIRK Methods","title":"IMEX SDIRK Methods","text":"IMEXEuler\r\nIMEXEulerARK\r\nKenCarp3\r\nKenCarp4\r\nKenCarp47\r\nKenCarp5\r\nKenCarp58\r\nESDIRK54I8L2SA\r\nESDIRK436L2SA2\r\nESDIRK437L2SA\r\nESDIRK547L2SA2\r\nESDIRK659L2SA","category":"page"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.IMEXEuler","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.IMEXEuler","text":"IMEXEuler(;kwargs...)\n\nThe one-step version of the IMEX multistep methods of\n\nUri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037\n\nWhen applied to a SplitODEProblem of the form\n\nu'(t) = f1(u) + f2(u)\n\nThe default IMEXEuler() method uses an update of the form\n\nunew = uold + dt * (f1(unew) + f2(uold))\n\nSee also SBDF, IMEXEulerARK.\n\n\n\n\n\n","category":"function"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.IMEXEulerARK","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.IMEXEulerARK","text":"IMEXEulerARK(;kwargs...)\n\nThe one-step version of the IMEX multistep methods of\n\nUri M. Ascher, Steven J. Ruuth, Brian T. R. Wetton. Implicit-Explicit Methods for Time-Dependent Partial Differential Equations. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 32(3), pp 797-823, 1995. doi: https://doi.org/10.1137/0732037\n\nWhen applied to a SplitODEProblem of the form\n\nu'(t) = f1(u) + f2(u)\n\nA classical additive Runge-Kutta method in the sense of Araújo, Murua, Sanz-Serna (1997) consisting of the implicit and the explicit Euler method given by\n\ny1 = uold + dt * f1(y1)\nunew = uold + dt * (f1(unew) + f2(y1))\n\nSee also SBDF, IMEXEuler.\n\n\n\n\n\n","category":"function"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.KenCarp3","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.KenCarp3","text":"@book{kennedy2001additive, title={Additive Runge-Kutta schemes for convection-diffusion-reaction equations}, author={Kennedy, Christopher Alan}, year={2001}, publisher={National Aeronautics and Space Administration, Langley Research Center} }\n\nKenCarp3: SDIRK Method An A-L stable stiffly-accurate 3rd order ESDIRK method with splitting\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.KenCarp4","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.KenCarp4","text":"@book{kennedy2001additive, title={Additive Runge-Kutta schemes for convection-diffusion-reaction equations}, author={Kennedy, Christopher Alan}, year={2001}, publisher={National Aeronautics and Space Administration, Langley Research Center} }\n\nKenCarp4: SDIRK Method An A-L stable stiffly-accurate 4th order ESDIRK method with splitting\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.KenCarp47","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.KenCarp47","text":"@article{kennedy2019higher, title={Higher-order additive Runge–Kutta schemes for ordinary differential equations}, author={Kennedy, Christopher A and Carpenter, Mark H}, journal={Applied Numerical Mathematics}, volume={136}, pages={183–205}, year={2019}, publisher={Elsevier} }\n\nKenCarp47: SDIRK Method An A-L stable stiffly-accurate 4th order seven-stage ESDIRK method with splitting\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.KenCarp5","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.KenCarp5","text":"@book{kennedy2001additive, title={Additive Runge-Kutta schemes for convection-diffusion-reaction equations}, author={Kennedy, Christopher Alan}, year={2001}, publisher={National Aeronautics and Space Administration, Langley Research Center} }\n\nKenCarp5: SDIRK Method An A-L stable stiffly-accurate 5th order ESDIRK method with splitting\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.KenCarp58","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.KenCarp58","text":"@article{kennedy2019higher, title={Higher-order additive Runge–Kutta schemes for ordinary differential equations}, author={Kennedy, Christopher A and Carpenter, Mark H}, journal={Applied Numerical Mathematics}, volume={136}, pages={183–205}, year={2019}, publisher={Elsevier} }\n\nKenCarp58: SDIRK Method An A-L stable stiffly-accurate 5th order eight-stage ESDIRK method with splitting\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.ESDIRK436L2SA2","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.ESDIRK436L2SA2","text":"@article{Kennedy2019DiagonallyIR, title={Diagonally implicit Runge–Kutta methods for stiff ODEs}, author={Christopher A. Kennedy and Mark H. Carpenter}, journal={Applied Numerical Mathematics}, year={2019}, volume={146}, pages={221-244} }\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.ESDIRK437L2SA","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.ESDIRK437L2SA","text":"@article{Kennedy2019DiagonallyIR, title={Diagonally implicit Runge–Kutta methods for stiff ODEs}, author={Christopher A. Kennedy and Mark H. Carpenter}, journal={Applied Numerical Mathematics}, year={2019}, volume={146}, pages={221-244} }\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.ESDIRK547L2SA2","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.ESDIRK547L2SA2","text":"@article{Kennedy2019DiagonallyIR, title={Diagonally implicit Runge–Kutta methods for stiff ODEs}, author={Christopher A. Kennedy and Mark H. Carpenter}, journal={Applied Numerical Mathematics}, year={2019}, volume={146}, pages={221-244} }\n\n\n\n\n\n","category":"type"},{"location":"imex/imex_sdirk/#OrdinaryDiffEq.ESDIRK659L2SA","page":"IMEX SDIRK Methods","title":"OrdinaryDiffEq.ESDIRK659L2SA","text":"@article{Kennedy2019DiagonallyIR, title={Diagonally implicit Runge–Kutta methods for stiff ODEs}, author={Christopher A. Kennedy and Mark H. Carpenter}, journal={Applied Numerical Mathematics}, year={2019}, volume={146}, pages={221-244}\n\nCurrently has STABILITY ISSUES, causing it to fail the adaptive tests. Check issue https://github.com/SciML/OrdinaryDiffEq.jl/issues/1933 for more details. }\n\n\n\n\n\n","category":"type"},{"location":"#OrdinaryDiffEq.jl","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl","text":"","category":"section"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"OrdinaryDiffEq.jl is a component package in the DifferentialEquations ecosystem. It holds the ordinary differential equation solvers and utilities. While completely independent and usable on its own, users interested in using this functionality should check out DifferentialEquations.jl.","category":"page"},{"location":"#Installation","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"Installation","text":"","category":"section"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"Assuming that you already have Julia correctly installed, it suffices to import OrdinaryDiffEq.jl in the standard way:","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"import Pkg; Pkg.add(\"OrdinaryDiffEq\")","category":"page"},{"location":"#Reproducibility","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"Reproducibility","text":"","category":"section"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"
    The documentation of this SciML package was built using these direct dependencies,","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"using Pkg # hide\nPkg.status() # hide","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"
    ","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"
    and using this machine and Julia version.","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"using InteractiveUtils # hide\nversioninfo() # hide","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"
    ","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"
    A more complete overview of all dependencies and their versions is also provided.","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"using Pkg # hide\nPkg.status(;mode = PKGMODE_MANIFEST) # hide","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"
    ","category":"page"},{"location":"","page":"OrdinaryDiffEq.jl: ODE solvers and utilities","title":"OrdinaryDiffEq.jl: ODE solvers and utilities","text":"You can also download the \nmanifest file and the\nproject file.","category":"page"},{"location":"stiff/sdirk/#Singly-Diagonally-Implicit-Runge-Kutta-(SDIRK)-Methods","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","text":"","category":"section"},{"location":"stiff/sdirk/","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","text":"ImplicitEuler\r\nImplicitMidpoint\r\nTrapezoid\r\nTRBDF2\r\nSDIRK2\r\nSDIRK22\r\nSSPSDIRK2\r\nKvaerno3\r\nCFNLIRK3\r\nCash4\r\nSFSDIRK4\r\nSFSDIRK5\r\nSFSDIRK6\r\nSFSDIRK7\r\nSFSDIRK8\r\nHairer4\r\nHairer42\r\nKvaerno4\r\nKvaerno5","category":"page"},{"location":"stiff/sdirk/#OrdinaryDiffEq.ImplicitEuler","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.ImplicitEuler","text":"ImplicitEuler: SDIRK Method A 1st order implicit solver. A-B-L-stable. Adaptive timestepping through a divided differences estimate via memory. Strong-stability preserving (SSP).\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.ImplicitMidpoint","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.ImplicitMidpoint","text":"ImplicitMidpoint: SDIRK Method A second order A-stable symplectic and symmetric implicit solver. Good for highly stiff equations which need symplectic integration.\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.Trapezoid","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.Trapezoid","text":"Andre Vladimirescu. 1994. The Spice Book. John Wiley & Sons, Inc., New York, NY, USA.\n\nTrapezoid: SDIRK Method A second order A-stable symmetric ESDIRK method. \"Almost symplectic\" without numerical dampening. Also known as Crank-Nicolson when applied to PDEs. Adaptive timestepping via divided differences approximation to the second derivative terms in the local truncation error estimate (the SPICE approximation strategy).\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.TRBDF2","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.TRBDF2","text":"@article{hosea1996analysis, title={Analysis and implementation of TR-BDF2}, author={Hosea, ME and Shampine, LF}, journal={Applied Numerical Mathematics}, volume={20}, number={1-2}, pages={21–37}, year={1996}, publisher={Elsevier} }\n\nTRBDF2: SDIRK Method A second order A-B-L-S-stable one-step ESDIRK method. Includes stiffness-robust error estimates for accurate adaptive timestepping, smoothed derivatives for highly stiff and oscillatory problems.\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.SDIRK2","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.SDIRK2","text":"@article{hindmarsh2005sundials, title={{SUNDIALS}: Suite of nonlinear and differential/algebraic equation solvers}, author={Hindmarsh, Alan C and Brown, Peter N and Grant, Keith E and Lee, Steven L and Serban, Radu and Shumaker, Dan E and Woodward, Carol S}, journal={ACM Transactions on Mathematical Software (TOMS)}, volume={31}, number={3}, pages={363–396}, year={2005}, publisher={ACM} }\n\nSDIRK2: SDIRK Method An A-B-L stable 2nd order SDIRK method\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.Kvaerno3","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.Kvaerno3","text":"@article{kvaerno2004singly, title={Singly diagonally implicit Runge–Kutta methods with an explicit first stage}, author={Kv{\\ae}rn{\\o}, Anne}, journal={BIT Numerical Mathematics}, volume={44}, number={3}, pages={489–502}, year={2004}, publisher={Springer} }\n\nKvaerno3: SDIRK Method An A-L stable stiffly-accurate 3rd order ESDIRK method\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.Cash4","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.Cash4","text":"@article{hindmarsh2005sundials, title={{SUNDIALS}: Suite of nonlinear and differential/algebraic equation solvers}, author={Hindmarsh, Alan C and Brown, Peter N and Grant, Keith E and Lee, Steven L and Serban, Radu and Shumaker, Dan E and Woodward, Carol S}, journal={ACM Transactions on Mathematical Software (TOMS)}, volume={31}, number={3}, pages={363–396}, year={2005}, publisher={ACM} }\n\nCash4: SDIRK Method An A-L stable 4th order SDIRK method\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.Hairer4","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.Hairer4","text":"E. Hairer, G. Wanner, Solving ordinary differential equations II, stiff and differential-algebraic problems. Computational mathematics (2nd revised ed.), Springer (1996)\n\nHairer4: SDIRK Method An A-L stable 4th order SDIRK method\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.Hairer42","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.Hairer42","text":"E. Hairer, G. Wanner, Solving ordinary differential equations II, stiff and differential-algebraic problems. Computational mathematics (2nd revised ed.), Springer (1996)\n\nHairer42: SDIRK Method An A-L stable 4th order SDIRK method\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.Kvaerno4","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.Kvaerno4","text":"@article{kvaerno2004singly, title={Singly diagonally implicit Runge–Kutta methods with an explicit first stage}, author={Kv{\\ae}rn{\\o}, Anne}, journal={BIT Numerical Mathematics}, volume={44}, number={3}, pages={489–502}, year={2004}, publisher={Springer} }\n\nKvaerno4: SDIRK Method An A-L stable stiffly-accurate 4th order ESDIRK method.\n\n\n\n\n\n","category":"type"},{"location":"stiff/sdirk/#OrdinaryDiffEq.Kvaerno5","page":"Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods","title":"OrdinaryDiffEq.Kvaerno5","text":"@article{kvaerno2004singly, title={Singly diagonally implicit Runge–Kutta methods with an explicit first stage}, author={Kv{\\ae}rn{\\o}, Anne}, journal={BIT Numerical Mathematics}, volume={44}, number={3}, pages={489–502}, year={2004}, publisher={Springer} }\n\nKvaerno5: SDIRK Method An A-L stable stiffly-accurate 5th order ESDIRK method\n\n\n\n\n\n","category":"type"}] +} diff --git a/previews/PR2081/semilinear/exponential_rk/index.html b/previews/PR2081/semilinear/exponential_rk/index.html new file mode 100644 index 0000000000..687a032785 --- /dev/null +++ b/previews/PR2081/semilinear/exponential_rk/index.html @@ -0,0 +1,6 @@ + +Exponential Runge-Kutta Integrators · OrdinaryDiffEq.jl
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    Exponential Runge-Kutta Integrators

    Missing docstring.

    Missing docstring for LawsonEuler. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for NorsettEuler. Check Documenter's build log for details.

    OrdinaryDiffEq.ETD2 — Type

    ETD2: Exponential Runge-Kutta Method Second order Exponential Time Differencing method (in development).

    source
    Missing docstring.

    Missing docstring for ETDRK2. Check Documenter's build log for details.

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    Missing docstring.

    Missing docstring for EPIRK5P2. Check Documenter's build log for details.

    diff --git a/previews/PR2081/semilinear/magnus/index.html b/previews/PR2081/semilinear/magnus/index.html new file mode 100644 index 0000000000..4165889b36 --- /dev/null +++ b/previews/PR2081/semilinear/magnus/index.html @@ -0,0 +1,6 @@ + +Magnus and Lie Group Integrators · OrdinaryDiffEq.jl
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    Magnus and Lie Group Integrators

    Missing docstring.

    Missing docstring for MagnusMidpoint. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for MagnusLeapfrog. Check Documenter's build log for details.

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    diff --git a/previews/PR2081/siteinfo.js b/previews/PR2081/siteinfo.js new file mode 100644 index 0000000000..7020f00402 --- /dev/null +++ b/previews/PR2081/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "previews/PR2081"; diff --git a/previews/PR2081/stiff/firk/index.html b/previews/PR2081/stiff/firk/index.html new file mode 100644 index 0000000000..4aa705a2e5 --- /dev/null +++ b/previews/PR2081/stiff/firk/index.html @@ -0,0 +1,6 @@ + +Fully Implicit Runge-Kutta (FIRK) Methods · OrdinaryDiffEq.jl
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    Fully Implicit Runge-Kutta (FIRK) Methods

    OrdinaryDiffEq.RadauIIA3 — Type

    @article{hairer1999stiff, title={Stiff differential equations solved by Radau methods}, author={Hairer, Ernst and Wanner, Gerhard}, journal={Journal of Computational and Applied Mathematics}, volume={111}, number={1-2}, pages={93–111}, year={1999}, publisher={Elsevier} }

    RadauIIA3: Fully-Implicit Runge-Kutta Method An A-B-L stable fully implicit Runge-Kutta method with internal tableau complex basis transform for efficiency.

    source
    OrdinaryDiffEq.RadauIIA5 — Type

    @article{hairer1999stiff, title={Stiff differential equations solved by Radau methods}, author={Hairer, Ernst and Wanner, Gerhard}, journal={Journal of Computational and Applied Mathematics}, volume={111}, number={1-2}, pages={93–111}, year={1999}, publisher={Elsevier} }

    RadauIIA5: Fully-Implicit Runge-Kutta Method An A-B-L stable fully implicit Runge-Kutta method with internal tableau complex basis transform for efficiency.

    source
    diff --git a/previews/PR2081/stiff/implicit_extrapolation/index.html b/previews/PR2081/stiff/implicit_extrapolation/index.html new file mode 100644 index 0000000000..c2080f43d1 --- /dev/null +++ b/previews/PR2081/stiff/implicit_extrapolation/index.html @@ -0,0 +1,6 @@ + +Implicit Extrapolation Methods · OrdinaryDiffEq.jl
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    Implicit Extrapolation Methods

    diff --git a/previews/PR2081/stiff/rosenbrock/index.html b/previews/PR2081/stiff/rosenbrock/index.html new file mode 100644 index 0000000000..5748031a2a --- /dev/null +++ b/previews/PR2081/stiff/rosenbrock/index.html @@ -0,0 +1,6 @@ + +Rosenbrock Methods · OrdinaryDiffEq.jl
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    Rosenbrock Methods

    Standard Rosenbrock Methods

    Missing docstring.

    Missing docstring for ROS3P. Check Documenter's build log for details.

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    Rosenbrock W-Methods

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    Missing docstring for Rosenbrock32. Check Documenter's build log for details.

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    Missing docstring for ROS34PW1a. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for ROS34PW1b. Check Documenter's build log for details.

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    Missing docstring for ROS34PW2. Check Documenter's build log for details.

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    Missing docstring for ROS34PW3. Check Documenter's build log for details.

    diff --git a/previews/PR2081/stiff/sdirk/index.html b/previews/PR2081/stiff/sdirk/index.html new file mode 100644 index 0000000000..a460cf21a1 --- /dev/null +++ b/previews/PR2081/stiff/sdirk/index.html @@ -0,0 +1,6 @@ + +Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods · OrdinaryDiffEq.jl
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    Singly-Diagonally Implicit Runge-Kutta (SDIRK) Methods

    OrdinaryDiffEq.ImplicitEuler — Type

    ImplicitEuler: SDIRK Method A 1st order implicit solver. A-B-L-stable. Adaptive timestepping through a divided differences estimate via memory. Strong-stability preserving (SSP).

    source
    OrdinaryDiffEq.ImplicitMidpoint — Type

    ImplicitMidpoint: SDIRK Method A second order A-stable symplectic and symmetric implicit solver. Good for highly stiff equations which need symplectic integration.

    source
    OrdinaryDiffEq.Trapezoid — Type

    Andre Vladimirescu. 1994. The Spice Book. John Wiley & Sons, Inc., New York, NY, USA.

    Trapezoid: SDIRK Method A second order A-stable symmetric ESDIRK method. "Almost symplectic" without numerical dampening. Also known as Crank-Nicolson when applied to PDEs. Adaptive timestepping via divided differences approximation to the second derivative terms in the local truncation error estimate (the SPICE approximation strategy).

    source
    OrdinaryDiffEq.TRBDF2 — Type

    @article{hosea1996analysis, title={Analysis and implementation of TR-BDF2}, author={Hosea, ME and Shampine, LF}, journal={Applied Numerical Mathematics}, volume={20}, number={1-2}, pages={21–37}, year={1996}, publisher={Elsevier} }

    TRBDF2: SDIRK Method A second order A-B-L-S-stable one-step ESDIRK method. Includes stiffness-robust error estimates for accurate adaptive timestepping, smoothed derivatives for highly stiff and oscillatory problems.

    source
    OrdinaryDiffEq.SDIRK2 — Type

    @article{hindmarsh2005sundials, title={{SUNDIALS}: Suite of nonlinear and differential/algebraic equation solvers}, author={Hindmarsh, Alan C and Brown, Peter N and Grant, Keith E and Lee, Steven L and Serban, Radu and Shumaker, Dan E and Woodward, Carol S}, journal={ACM Transactions on Mathematical Software (TOMS)}, volume={31}, number={3}, pages={363–396}, year={2005}, publisher={ACM} }

    SDIRK2: SDIRK Method An A-B-L stable 2nd order SDIRK method

    source
    Missing docstring.

    Missing docstring for SDIRK22. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for SSPSDIRK2. Check Documenter's build log for details.

    OrdinaryDiffEq.Kvaerno3 — Type

    @article{kvaerno2004singly, title={Singly diagonally implicit Runge–Kutta methods with an explicit first stage}, author={Kv{\ae}rn{\o}, Anne}, journal={BIT Numerical Mathematics}, volume={44}, number={3}, pages={489–502}, year={2004}, publisher={Springer} }

    Kvaerno3: SDIRK Method An A-L stable stiffly-accurate 3rd order ESDIRK method

    source
    Missing docstring.

    Missing docstring for CFNLIRK3. Check Documenter's build log for details.

    OrdinaryDiffEq.Cash4 — Type

    @article{hindmarsh2005sundials, title={{SUNDIALS}: Suite of nonlinear and differential/algebraic equation solvers}, author={Hindmarsh, Alan C and Brown, Peter N and Grant, Keith E and Lee, Steven L and Serban, Radu and Shumaker, Dan E and Woodward, Carol S}, journal={ACM Transactions on Mathematical Software (TOMS)}, volume={31}, number={3}, pages={363–396}, year={2005}, publisher={ACM} }

    Cash4: SDIRK Method An A-L stable 4th order SDIRK method

    source
    Missing docstring.

    Missing docstring for SFSDIRK4. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for SFSDIRK5. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for SFSDIRK6. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for SFSDIRK7. Check Documenter's build log for details.

    Missing docstring.

    Missing docstring for SFSDIRK8. Check Documenter's build log for details.

    OrdinaryDiffEq.Hairer4 — Type

    E. Hairer, G. Wanner, Solving ordinary differential equations II, stiff and differential-algebraic problems. Computational mathematics (2nd revised ed.), Springer (1996)

    Hairer4: SDIRK Method An A-L stable 4th order SDIRK method

    source
    OrdinaryDiffEq.Hairer42 — Type

    E. Hairer, G. Wanner, Solving ordinary differential equations II, stiff and differential-algebraic problems. Computational mathematics (2nd revised ed.), Springer (1996)

    Hairer42: SDIRK Method An A-L stable 4th order SDIRK method

    source
    OrdinaryDiffEq.Kvaerno4 — Type

    @article{kvaerno2004singly, title={Singly diagonally implicit Runge–Kutta methods with an explicit first stage}, author={Kv{\ae}rn{\o}, Anne}, journal={BIT Numerical Mathematics}, volume={44}, number={3}, pages={489–502}, year={2004}, publisher={Springer} }

    Kvaerno4: SDIRK Method An A-L stable stiffly-accurate 4th order ESDIRK method.

    source
    OrdinaryDiffEq.Kvaerno5 — Type

    @article{kvaerno2004singly, title={Singly diagonally implicit Runge–Kutta methods with an explicit first stage}, author={Kv{\ae}rn{\o}, Anne}, journal={BIT Numerical Mathematics}, volume={44}, number={3}, pages={489–502}, year={2004}, publisher={Springer} }

    Kvaerno5: SDIRK Method An A-L stable stiffly-accurate 5th order ESDIRK method

    source
    diff --git a/previews/PR2081/stiff/stabilized_rk/index.html b/previews/PR2081/stiff/stabilized_rk/index.html new file mode 100644 index 0000000000..fb353ab843 --- /dev/null +++ b/previews/PR2081/stiff/stabilized_rk/index.html @@ -0,0 +1,6 @@ + +Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev) · OrdinaryDiffEq.jl
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    Stabilized Runge-Kutta Methods (Runge-Kutta-Chebyshev)

    Explicit Stabilized Runge-Kutta Methods

    Explicit stabilized methods utilize an upper bound on the spectral radius of the Jacobian. Users can supply an upper bound by specifying the keyword argument eigen_est, for example

    `eigen_est = (integrator) -> integrator.eigen_est = upper_bound`

    The methods ROCK2 and ROCK4 also include keyword arguments min_stages and max_stages, which specify upper and lower bounds on the adaptively chosen number of stages for stability.

    OrdinaryDiffEq.ROCK2 — Type

    Assyr Abdulle, Alexei A. Medovikov. Second Order Chebyshev Methods based on Orthogonal Polynomials. Numerische Mathematik, 90 (1), pp 1-18, 2001. doi: https://dx.doi.org/10.1007/s002110100292

    ROCK2: Stabilized Explicit Method. Second order stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues and is smoothened to allow for moderate sized complex eigenvalues.

    This method takes optional keyword arguments min_stages, max_stages, and eigen_est. The function eigen_est should be of the form

    eigen_est = (integrator) -> integrator.eigen_est = upper_bound,

    where upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.

    source
    OrdinaryDiffEq.ROCK4 — Type
    ROCK4(; min_stages = 0, max_stages = 152, eigen_est = nothing)

    Assyr Abdulle. Fourth Order Chebyshev Methods With Recurrence Relation. 2002 Society for Industrial and Applied Mathematics Journal on Scientific Computing, 23(6), pp 2041-2054, 2001. doi: https://doi.org/10.1137/S1064827500379549

    ROCK4: Stabilized Explicit Method. Fourth order stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues and is smoothened to allow for moderate sized complex eigenvalues.

    This method takes optional keyword arguments min_stages, max_stages, and eigen_est. The function eigen_est should be of the form

    eigen_est = (integrator) -> integrator.eigen_est = upper_bound,

    where upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.

    source
    Missing docstring.

    Missing docstring for SERK2. Check Documenter's build log for details.

    OrdinaryDiffEq.ESERK4 — Type
    ESERK4(; eigen_est = nothing)

    J. Martín-Vaquero, B. Kleefeld. Extrapolated stabilized explicit Runge-Kutta methods, Journal of Computational Physics, 326, pp 141-155, 2016. doi: https://doi.org/10.1016/j.jcp.2016.08.042.

    ESERK4: Stabilized Explicit Method. Fourth order extrapolated stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues and is smoothened to allow for moderate sized complex eigenvalues.

    This method takes the keyword argument eigen_est of the form

    eigen_est = (integrator) -> integrator.eigen_est = upper_bound,

    where upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.

    source
    OrdinaryDiffEq.ESERK5 — Type
    ESERK5(; eigen_est = nothing)

    J. Martín-Vaquero, A. Kleefeld. ESERK5: A fifth-order extrapolated stabilized explicit Runge-Kutta method, Journal of Computational and Applied Mathematics, 356, pp 22-36, 2019. doi: https://doi.org/10.1016/j.cam.2019.01.040.

    ESERK5: Stabilized Explicit Method. Fifth order extrapolated stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues and is smoothened to allow for moderate sized complex eigenvalues.

    This method takes the keyword argument eigen_est of the form

    eigen_est = (integrator) -> integrator.eigen_est = upper_bound,

    where upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.

    source
    OrdinaryDiffEq.RKC — Type
    RKC(; eigen_est = nothing)

    B. P. Sommeijer, L. F. Shampine, J. G. Verwer. RKC: An Explicit Solver for Parabolic PDEs, Journal of Computational and Applied Mathematics, 88(2), pp 315-326, 1998. doi: https://doi.org/10.1016/S0377-0427(97)00219-7

    RKC: Stabilized Explicit Method. Second order stabilized Runge-Kutta method. Exhibits high stability for real eigenvalues.

    This method takes the keyword argument eigen_est of the form

    eigen_est = (integrator) -> integrator.eigen_est = upper_bound,

    where upper_bound is an estimated upper bound on the spectral radius of the Jacobian matrix. If eigen_est is not provided, upper_bound will be estimated using the power iteration.

    source

    Implicit Stabilized Runge-Kutta Methods

    Missing docstring.

    Missing docstring for IRKC. Check Documenter's build log for details.

    diff --git a/previews/PR2081/stiff/stiff_multistep/index.html b/previews/PR2081/stiff/stiff_multistep/index.html new file mode 100644 index 0000000000..ec4eb11d97 --- /dev/null +++ b/previews/PR2081/stiff/stiff_multistep/index.html @@ -0,0 +1,6 @@ + +Multistep Methods for Stiff Equations · OrdinaryDiffEq.jl
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    Multistep Methods for Stiff Equations

    OrdinaryDiffEq.QNDF1 — Type

    QNDF1: Multistep Method An adaptive order 1 quasi-constant timestep L-stable numerical differentiation function (NDF) method. Optional parameter kappa defaults to Shampine's accuracy-optimal -0.1850.

    See also QNDF.

    source
    OrdinaryDiffEq.QNDF2 — Type

    QNDF2: Multistep Method An adaptive order 2 quasi-constant timestep L-stable numerical differentiation function (NDF) method.

    See also QNDF.

    source
    OrdinaryDiffEq.ABDF2 — Type

    E. Alberdi Celayaa, J. J. Anza Aguirrezabalab, P. Chatzipantelidisc. Implementation of an Adaptive BDF2 Formula and Comparison with The MATLAB Ode15s. Procedia Computer Science, 29, pp 1014-1026, 2014. doi: https://doi.org/10.1016/j.procs.2014.05.091

    ABDF2: Multistep Method An adaptive order 2 L-stable fixed leading coefficient multistep BDF method.

    source
    OrdinaryDiffEq.QNDF — Type

    QNDF: Multistep Method An adaptive order quasi-constant timestep NDF method. Utilizes Shampine's accuracy-optimal kappa values as defaults (has a keyword argument for a tuple of kappa coefficients).

    @article{shampine1997matlab, title={The matlab ode suite}, author={Shampine, Lawrence F and Reichelt, Mark W}, journal={SIAM journal on scientific computing}, volume={18}, number={1}, pages={1–22}, year={1997}, publisher={SIAM} }

    source
    OrdinaryDiffEq.FBDF — Type

    FBDF: Fixed leading coefficient BDF

    An adaptive order quasi-constant timestep NDF method. Utilizes Shampine's accuracy-optimal kappa values as defaults (has a keyword argument for a tuple of kappa coefficients).

    @article{shampine2002solving, title={Solving 0= F (t, y (t), y′(t)) in Matlab}, author={Shampine, Lawrence F}, year={2002}, publisher={Walter de Gruyter GmbH \& Co. KG} }

    source
    OrdinaryDiffEq.MEBDF2 — Type

    MEBDF2: Multistep Method The second order Modified Extended BDF method, which has improved stability properties over the standard BDF. Fixed timestep only.

    source
    diff --git a/previews/PR2081/usage/index.html b/previews/PR2081/usage/index.html new file mode 100644 index 0000000000..a1af2dfabb --- /dev/null +++ b/previews/PR2081/usage/index.html @@ -0,0 +1,41 @@ + +Usage · OrdinaryDiffEq.jl
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    Usage

    OrdinaryDiffEq.jl is part of the SciML common interface, but can be used independently of DifferentialEquations.jl. The only requirement is that the user passes an OrdinaryDiffEq.jl algorithm to solve. For example, we can solve the ODE tutorial from the docs using the Tsit5() algorithm:

    using OrdinaryDiffEq
+f(u,p,t) = 1.01*u
+u0=1/2
+tspan = (0.0,1.0)
+prob = ODEProblem(f,u0,tspan)
+sol = solve(prob,Tsit5(),reltol=1e-8,abstol=1e-8)
+using Plots
+plot(sol,linewidth=5,title="Solution to the linear ODE with a thick line",
+     xaxis="Time (t)",yaxis="u(t) (in μm)",label="My Thick Line!") # legend=false
+plot!(sol.t, t->0.5*exp(1.01t),lw=3,ls=:dash,label="True Solution!")

    That example uses the out-of-place syntax f(u,p,t), while the inplace syntax (more efficient for systems of equations) is shown in the Lorenz example:

    using OrdinaryDiffEq
+function lorenz(du,u,p,t)
+ du[1] = 10.0(u[2]-u[1])
+ du[2] = u[1]*(28.0-u[3]) - u[2]
+ du[3] = u[1]*u[2] - (8/3)*u[3]
+end
+u0 = [1.0;0.0;0.0]
+tspan = (0.0,100.0)
+prob = ODEProblem(lorenz,u0,tspan)
+sol = solve(prob,Tsit5())
+using Plots; plot(sol,vars=(1,2,3))

    Very fast static array versions can be specifically compiled to the size of your model. For example:

    using OrdinaryDiffEq, StaticArrays
+function lorenz(u,p,t)
+ SA[10.0(u[2]-u[1]),u[1]*(28.0-u[3]) - u[2],u[1]*u[2] - (8/3)*u[3]]
+end
+u0 = SA[1.0;0.0;0.0]
+tspan = (0.0,100.0)
+prob = ODEProblem(lorenz,u0,tspan)
+sol = solve(prob,Tsit5())

    For “refined ODEs”, like dynamical equations and SecondOrderODEProblems, refer to the DiffEqDocs. For example, in DiffEqTutorials.jl we show how to solve equations of motion using symplectic methods:

    function HH_acceleration(dv,v,u,p,t)
+    x,y  = u
+    dx,dy = dv
+    dv[1] = -x - 2x*y
+    dv[2] = y^2 - y -x^2
+end
+initial_positions = [0.0,0.1]
+initial_velocities = [0.5,0.0]
+prob = SecondOrderODEProblem(HH_acceleration,initial_velocities,initial_positions,tspan)
+sol2 = solve(prob, KahanLi8(), dt=1/10);

    Other refined forms are IMEX and semi-linear ODEs (for exponential integrators).

    Available Solvers

    For the list of available solvers, please refer to the DifferentialEquations.jl ODE Solvers, Dynamical ODE Solvers, and the Split ODE Solvers pages.