Documentation for 2a076c1b03

2026-05-16 14:14:27 +08:00 · 2022-06-09 15:19:34 +00:00
parent 44595908ec
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4173 changed files with 15438 additions and 15542 deletions
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 <div class="textblock"><p >Solve a multivariable first order <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation" target="_blank">ordinary differential equation (ODEs)</a> using <a href="https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations#Euler_method" target="_blank">forward Euler method</a> </p>
 <dl class="section author"><dt>Authors</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a></dd></dl>
 <p>The ODE being solved is: </p><p class="formulaDsp">
-\begin{eqnarray*} \dot{u} &amp;=&amp; v\\ \dot{v} &amp;=&amp; -\omega^2 u\\ \omega &amp;=&amp; 1\\ [x_0, u_0, v_0] &amp;=&amp; [0,1,0]\qquad\ldots\text{(initial values)} \end{eqnarray*}
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 <p> The exact solution for the above problem is: </p><p class="formulaDsp">
-\begin{eqnarray*} u(x) &amp;=&amp; \cos(x)\\ v(x) &amp;=&amp; -\sin(x)\\ \end{eqnarray*}
+\begin{eqnarray*}
+u(x) &amp;=&amp; \cos(x)\\
+v(x) &amp;=&amp; -\sin(x)\\
+\end{eqnarray*}
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 <p> The computation results are stored to a text file <code>forward_euler.csv</code> and the exact soltuion results in <code>exact.csv</code> for comparison. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/ode_forward_euler.svg" alt="Implementation solution" style="pointer-events: none;" class="inline"/></p>
 <p >To implement <a href="https://en.wikipedia.org/wiki/Van_der_Pol_oscillator" target="_blank">Van der Pol oscillator</a>, change the <a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe" title="Problem statement for a system with first-order differential equations. Updates the system differenti...">problem</a> function to: </p><div class="fragment"><div class="line"><span class="keyword">const</span> <span class="keywordtype">double</span> mu = 2.0;</div>
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