Merge branch 'main' of https://github.com/aslab-math-ui/modul-prak

docs/listings.json

@@ -34,6 +34,7 @@
   {
     "listing": "/semuahalaman/modulprak/2024/ganjil/molin/molin2024.html",
     "items": [
+      "/semuahalaman/modulprak/2024/ganjil/molin/modul6.html",
       "/semuahalaman/modulprak/2024/ganjil/molin/modul5.html",
       "/semuahalaman/modulprak/2024/ganjil/molin/modul4.html",
       "/semuahalaman/modulprak/2024/ganjil/molin/modul3.html",

docs/semuahalaman/modulprak/2023/genap/pdnum/module/week-02p2.html

@@ -220,7 +220,7 @@ <h2 class="anchored" data-anchor-id="metode-euler">Metode Euler</h2>
 <p>dengan <span class="math inline">\(n+1\in \mathbb{N}\)</span> menyatakan banyaknya titik nantinya.</p>
 <p>Solusi kita akan berupa titik yang nantinya dapat menggunakan interpolasi untuk nilai yang tidak dimuat di <span class="math inline">\(w_i\)</span></p>
 <p>Algoritma untuk metode Euler adalah sebagai berikut:</p>
-<div id="a24bb18b" class="cell">
+<div id="5a3aa30b" class="cell">
 <div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>function [t, w] <span class="op">=</span> euler(f, a, b, n, alpha)</span>
 <span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>  h <span class="op">=</span> (b <span class="op">-</span> a) <span class="op">/</span> n<span class="op">;</span></span>
 <span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>  t <span class="op">=</span> zeros(n <span class="op">+</span> <span class="dv">1</span>, <span class="dv">1</span>)<span class="op">;</span></span>
@@ -241,7 +241,7 @@ <h2 class="anchored" data-anchor-id="metode-euler">Metode Euler</h2>
 \end{aligned}
 \]</span></p>
 <p>maka kita dapat mendefinisikan <code>f=@(t, y)\left(y-t^{\wedge} 2+1\right)</code>, a=0, b=2, dan alpha <span class="math inline">\(=0.5\)</span> (@ disini menyatakan fungsi anonim yang cara kerjanya mirip dengan fungsi lambda pada Python), sehingga untuk <span class="math inline">\(n=10\)</span>, diperoleh kode sebagai berikut:</p>
-<div id="1184db83" class="cell">
+<div id="a2c9ea06" class="cell">
 <div class="sourceCode cell-code" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>f <span class="op">=</span> <span class="op">@</span>(t, y) (y<span class="op">-</span>t<span class="op">^</span><span class="dv">2</span> <span class="op">+</span> <span class="dv">1</span>)<span class="op">;</span></span>
 <span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> <span class="dv">0</span><span class="op">;</span></span>
 <span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>b <span class="op">=</span> <span class="dv">2</span><span class="op">;</span></span>
@@ -251,7 +251,7 @@ <h2 class="anchored" data-anchor-id="metode-euler">Metode Euler</h2>
 </div>
 <p>Untuk visualisasinya, kita akan membuat plot dari hasil yang kita peroleh. Sebagai referensi, solusi eksak dari PD tersebut adalah <span class="math inline">\(y(t)=(t+1)^2- 0.5 e^t\)</span></p>
 <p>Kita tambahkan kode berikut pada file:$</p>
-<div id="c3aa5404" class="cell">
+<div id="0107df5a" class="cell">
 <div class="sourceCode cell-code" id="cb3"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>sln <span class="op">=</span> <span class="op">@</span>(t) (t <span class="op">+</span> <span class="dv">1</span>)<span class="op">^</span><span class="dv">2</span> <span class="op">-</span> <span class="fl">0.5</span> <span class="op">*</span> exp(t)<span class="op">;</span></span>
 <span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>fplot(sln, [<span class="dv">0</span>, <span class="dv">2</span>], <span class="st">'b'</span>)<span class="op">;</span></span>
 <span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>hold on<span class="op">;</span></span>
@@ -301,7 +301,7 @@ <h2 class="anchored" data-anchor-id="metode-runge-kutta-dan-variasinya">Metode R
 \]</span></li>
 </ol>
 <p>Berikut adalah list algoritmanya.</p>
-<div id="5504f318" class="cell">
+<div id="a2e93949" class="cell">
 <div class="sourceCode cell-code" id="cb4"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>function [t, w] <span class="op">=</span> midpoint(f, a, b, n, alpha)</span>
 <span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>  h <span class="op">=</span> (b <span class="op">-</span> a) <span class="op">/</span> n<span class="op">;</span></span>
 <span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>  t <span class="op">=</span> zeros(n <span class="op">+</span> <span class="dv">1</span>, <span class="dv">1</span>)<span class="op">;</span></span>
@@ -316,7 +316,7 @@ <h2 class="anchored" data-anchor-id="metode-runge-kutta-dan-variasinya">Metode R
 <span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a>  endfor</span>
 <span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a>endfunction</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
-<div id="31fea46e" class="cell">
+<div id="0af779c4" class="cell">
 <div class="sourceCode cell-code" id="cb5"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>function [t, w] <span class="op">=</span> modeuler(f, a, b, n, alpha)</span>
 <span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>  h <span class="op">=</span> (b <span class="op">-</span> a) <span class="op">/</span> n<span class="op">;</span></span>
 <span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>  t <span class="op">=</span> zeros(n <span class="op">+</span> <span class="dv">1</span>, <span class="dv">1</span>)<span class="op">;</span></span>
@@ -331,7 +331,7 @@ <h2 class="anchored" data-anchor-id="metode-runge-kutta-dan-variasinya">Metode R
 <span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a>  endfor</span>
 <span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a>endfunction</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
-<div id="3e648713" class="cell">
+<div id="39e552ac" class="cell">
 <div class="sourceCode cell-code" id="cb6"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>function [t, w] <span class="op">=</span> heun(f, a, b, n, alpha)</span>
 <span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>  h <span class="op">=</span> (b <span class="op">-</span> a) <span class="op">/</span> n<span class="op">;</span></span>
 <span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>  t <span class="op">=</span> zeros(n <span class="op">+</span> <span class="dv">1</span>, <span class="dv">1</span>)<span class="op">;</span></span>
@@ -348,7 +348,7 @@ <h2 class="anchored" data-anchor-id="metode-runge-kutta-dan-variasinya">Metode R
 <span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a>  endfor</span>
 <span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a>endfunction</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
-<div id="c0204170" class="cell">
+<div id="8d5d8029" class="cell">
 <div class="sourceCode cell-code" id="cb7"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>function [t, w] <span class="op">=</span> rko4(f, a, b, n, alpha)</span>
 <span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>  h <span class="op">=</span> (b <span class="op">-</span> a) <span class="op">/</span> n<span class="op">;</span></span>
 <span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>  t <span class="op">=</span> zeros(n <span class="op">+</span> <span class="dv">1</span>, <span class="dv">1</span>)<span class="op">;</span></span>
@@ -365,7 +365,7 @@ <h2 class="anchored" data-anchor-id="metode-runge-kutta-dan-variasinya">Metode R
 <span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a>  endfor</span>
 <span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a>endfunction</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
-<div id="37914d67" class="cell">
+<div id="db4c5587" class="cell">
 <div class="sourceCode cell-code" id="cb8"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>f <span class="op">=</span> <span class="op">@</span>(t, y) (y <span class="op">-</span> t <span class="op">^</span> <span class="dv">2</span> <span class="op">+</span> <span class="dv">1</span>)<span class="op">;</span></span>
 <span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> <span class="dv">0</span><span class="op">;</span></span>
 <span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>b <span class="op">=</span> <span class="dv">2</span><span class="op">;</span></span>

docs/semuahalaman/modulprak/2023/genap/pdnum/module/week-03.html

@@ -256,7 +256,7 @@ <h3 class="anchored" data-anchor-id="multistep-eksplisit-metode-n-step-adams-bas
 \end{gathered}
 \]</span></p>
 <p>program untuk two-step Adams-Bashforth:</p>
-<div id="5aff5b7c" class="cell">
+<div id="caaec26d" class="cell">
 <div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="op">%</span>function_file</span>
 <span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>function [t, w] <span class="op">=</span> adams2(f, a, b, n, alpha)</span>
 <span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>  <span class="op">%</span> Inisiasi variabel awal</span>
@@ -285,7 +285,7 @@ <h3 class="anchored" data-anchor-id="multistep-eksplisit-metode-n-step-adams-bas
 <span id="cb1-26"><a href="#cb1-26" aria-hidden="true" tabindex="-1"></a>endfunction</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div>
 <p>Berikut ini adalah contoh pengerjaaannya dengan menggunakan metode two-step Adams-Bashforth.</p>
-<div id="96638cff" class="cell">
+<div id="87c27c37" class="cell">
 <div class="sourceCode cell-code" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="op">%</span>script <span class="bu">file</span></span>
 <span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>f <span class="op">=</span> <span class="op">@</span>(t, y) (y <span class="op">-</span> t <span class="op">^</span> <span class="dv">2</span> <span class="op">+</span> <span class="dv">1</span>)<span class="op">;</span></span>
 <span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> <span class="dv">0</span><span class="op">;</span></span>
@@ -332,7 +332,7 @@ <h3 class="anchored" data-anchor-id="multistep-implisit-metode-n-step-adams-moul
 \end{aligned}
 \]</span></p>
 <p>Bentuk umum program yang akan dihasilkan</p>
-<div id="c2a50060" class="cell">
+<div id="7fcaec6b" class="cell">
 <div class="sourceCode cell-code" id="cb3"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="op">%</span>function_file</span>
 <span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>function [t, w] <span class="op">=</span> adam<span class="op">-</span>moulton<span class="op">-</span>general(f, a, b, n, alpha)</span>
 <span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>  [</span>
@@ -368,7 +368,7 @@ <h3 class="anchored" data-anchor-id="multistep-metode-n-step-adams-moulton-bashf
 <h2 class="anchored" data-anchor-id="solusi-numerik-sistem-persamaan-differential">solusi numerik sistem Persamaan Differential</h2>
 <section id="rungge-kutta-untuk-sistem-persamaan-differential-vectorize" class="level3">
 <h3 class="anchored" data-anchor-id="rungge-kutta-untuk-sistem-persamaan-differential-vectorize">Rungge kutta untuk sistem persamaan differential (vectorize)</h3>
-<div id="9074ac87" class="cell">
+<div id="ff23fe59" class="cell">
 <div class="sourceCode cell-code" id="cb4"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="op">%</span>function_file</span>
 <span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>function [t,w] <span class="op">=</span> rk4_sys(f, a, b, n, y0)</span>
 <span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>  <span class="op">%</span>f :differential equation y_p <span class="op">=</span> f(t,y)</span>
@@ -398,7 +398,7 @@ <h3 class="anchored" data-anchor-id="rungge-kutta-untuk-sistem-persamaan-differe
 &amp; I_2^{\prime}=f_2\left(t, I_1, I_2\right)=0.6 I_1^{\prime}-0.2 I_2=-2.4 I_1+1.6 I_2+3.6, \quad I_2(0)=0 .
 \end{aligned}
 \]</span> Persamasalahan berikut akan dikerjakan dengan <code>rk4_sys</code> dengan mengunakan titik awal <span class="math inline">\(t_0=0\)</span> dan <span class="math inline">\(t_{n+1}=1\)</span> dengan <span class="math inline">\(n=10\)</span> partisi.</p>
-<div id="b81ffa2d" class="cell">
+<div id="ecc232f7" class="cell">
 <div class="sourceCode cell-code" id="cb5"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="op">%</span>script <span class="bu">file</span></span>
 <span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>f<span class="op">=@</span>(t, I) [<span class="op">-</span><span class="dv">4</span> <span class="op">*</span> I(<span class="dv">1</span>)<span class="op">+</span> <span class="dv">3</span> <span class="op">*</span> I(<span class="dv">2</span>)<span class="op">+</span><span class="dv">6</span> <span class="op">;</span> <span class="op">-</span><span class="fl">2.4</span><span class="op">*</span>I(<span class="dv">1</span>) <span class="op">+</span> <span class="fl">1.6</span> <span class="op">*</span> I(<span class="dv">2</span>)<span class="op">+</span><span class="fl">3.6</span>] <span class="op">%</span> fungsi</span>
 <span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="op">%</span> perhatikan bahwa  I addalah vektor (hence ada I(<span class="dv">1</span>) dan I(<span class="dv">2</span>))</span>
@@ -416,7 +416,7 @@ <h3 class="anchored" data-anchor-id="rungge-kutta-untuk-sistem-persamaan-differe
 </section>
 <section id="predictor-corrector-metode-adams-bashforth-moulton-2-step-untuk-sistem-persamaan-differential-vectorize" class="level3">
 <h3 class="anchored" data-anchor-id="predictor-corrector-metode-adams-bashforth-moulton-2-step-untuk-sistem-persamaan-differential-vectorize">Predictor-Corrector: Metode Adams-Bashforth-Moulton 2-step untuk sistem persamaan differential (vectorize)</h3>
-<div id="73571592" class="cell">
+<div id="d438819e" class="cell">
 <div class="sourceCode cell-code" id="cb6"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="op">%</span> the multi<span class="op">-</span>step second order method Adams<span class="op">-</span>Bashforth<span class="op">-</span>Moulton </span>
 <span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a></span>
 <span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="op">%</span>function_file</span>