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jcponce committed Jul 31, 2023
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Expand Up @@ -1264,17 +1264,22 @@ <h5>1 Ordinary Differential Equations</h5>
<p>
<span>
Matlab has some more sophisticated numerical methods for solving ODEs than
Euler's method.
Matlab's <span style="color:blue">ode45</span> uses a
<a href="https://mathworld.wolfram.com/Runge-KuttaMethod.html" target="_blank">Runge-Kutta fourth-order integration
technique</a>. To use it you need to write two little programs. The first
one, say <tt>logistic.m</tt>,
defines the differential equation
Euler's method.
</span>
<span class="fragment" data-fragment-index="1">
Matlab's <span style="color:blue">ode45</span> uses a
<a href="https://mathworld.wolfram.com/Runge-KuttaMethod.html" target="_blank">Runge-Kutta fourth-order integration
technique</a>.
</span>
<span class="fragment" data-fragment-index="2">
To use it you need to write two little programs. The first
one, say <tt>logistic.m</tt>,
defines the differential equation
</span>
</p>
</div>
</div>
<div style="font-size:110%">
<div style="font-size:120%;margin-top:-10px" class="fragment" data-fragment-index="2">
<pre><code data-trim data-noescape data-line-numbers="1-2">
function dy = logistic(t, y)
dy = y * (1 - y);
Expand All @@ -1284,14 +1289,14 @@ <h5>1 Ordinary Differential Equations</h5>

<div class="left-txt">
<p>
<span>
<span class="fragment" data-fragment-index="3">
The second program will numerically solve the ODE and plot your
solution.
</span>
</p>
</div>
</div>
<div style="font-size:110%">
<div style="font-size:120%;margin-top:-10px" class="fragment" data-fragment-index="3">
<pre><code data-trim data-noescape data-line-numbers="1-4">
y0 = 0.1;
tfinal = 6;
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