From a9c4541110ee10c8018053f224f0272126e3844a Mon Sep 17 00:00:00 2001 From: Warisa Date: Sat, 30 Nov 2024 15:02:44 +0100 Subject: [PATCH] get rid of the numbered list --- docs/src/time_integration.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/docs/src/time_integration.md b/docs/src/time_integration.md index 9a200646f52..6f07d3011bd 100644 --- a/docs/src/time_integration.md +++ b/docs/src/time_integration.md @@ -81,7 +81,7 @@ Nevertheless, due to their optimized stability properties and low-storage nature In this tutorial, we will demonstrate how you can use the second-order PERK time integrator. You need the packages `Convex.jl` and `ECOS.jl`, so be sure they are added to your environment. -1. First, you need to load the necessary packages: +First, you need to load the necessary packages: ```@example PERK-example-1 using Convex, ECOS @@ -89,7 +89,7 @@ using OrdinaryDiffEq using Trixi ``` -2. Define the ODE problem and the semidiscretization setup. For this example, we will use a simple advection problem. +Then, define the ODE problem and the semidiscretization setup. For this example, we will use a simple advection problem. ```@example PERK-example-1 # Define the mesh @@ -114,7 +114,7 @@ semi = SemidiscretizationHyperbolic(mesh, solver) ``` -3. Define the necessary [callbacks](@ref callbacks-id) for the simulation. Callbacks are used to perform actions at specific points during the integration process. +After that, we will define the necessary [callbacks](@ref callbacks-id) for the simulation. Callbacks are used to perform actions at specific points during the integration process. ```@example PERK-example-1 # Define some standard callbacks @@ -131,7 +131,7 @@ callbacks = CallbackSet(summary_callback, stepsize_callback) ``` -4. Define the ODE problem by specifying the time span over which the ODE will be solved. +Now, we define the ODE problem by specifying the time span over which the ODE will be solved. The `tspan` parameter is a tuple `(t_start, t_end)` that defines the start and end times for the simulation. The `semidiscretize` function is used to create the ODE problem from the simulation setup. @@ -143,7 +143,7 @@ tspan = (0.0, 1.0) ode = semidiscretize(semi, tspan) ``` -5. In this step we will construct the time integrator. In order to do this, you need the following components: +Next, we will construct the time integrator. In order to do this, you need the following components: - Number of stages: The number of stages $S$ in the Runge-Kutta method. In this example, we use `6` stages. @@ -161,7 +161,7 @@ ode = semidiscretize(semi, tspan) ode_algorithm = Trixi.PairedExplicitRK2(6, tspan, semi) ``` -6. With everything now set up, you can now use `Trixi.solve` to solve the ODE problem. The `solve` function takes the ODE problem, the time integrator, and some options such as the time step (`dt`), whether to save every step (`save_everystep`), and the callbacks. +With everything now set up, you can now use `Trixi.solve` to solve the ODE problem. The `solve` function takes the ODE problem, the time integrator, and some options such as the time step (`dt`), whether to save every step (`save_everystep`), and the callbacks. ```@example PERK-example-1 # Solve the ODE problem using PERK2 @@ -170,7 +170,7 @@ sol = Trixi.solve(ode, ode_algorithm, save_everystep = false, callback = callbacks) ``` -7. Advanced constructors: +##### Advanced constructors: There are two additional constructors for the `PairedExplicitRK2` method besides the one taking in a semidiscretization `semi`: - `PairedExplicitRK2(num_stages, base_path_monomial_coeffs::AbstractString)` constructs a `num_stages`-stage method from the given optimal monomial_coeffs $\boldsymbol \alpha$. These are expected to be present in the provided directory in the form of a `gamma_.txt` file, where `` is the number of stages `num_stages`.