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<div class="headertitle"><div class="title">ode_semi_implicit_euler.cpp File Reference</div></div>
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Include dependency graph for ode_semi_implicit_euler.cpp:</div>
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<p><a href="../../d3/d06/ode__semi__implicit__euler_8cpp_source.html">Go to the source code of this file.</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
<tr class="heading"><td colspan="2"><h2 id="header-func-members" class="groupheader"><a id="func-members" name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:abaeae8f62a018d197f0187a1c80a90fe" id="r_abaeae8f62a018d197f0187a1c80a90fe"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#abaeae8f62a018d197f0187a1c80a90fe">problem</a> (const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</td></tr>
<tr class="memdesc:abaeae8f62a018d197f0187a1c80a90fe"><td class="mdescLeft">&#160;</td><td class="mdescRight">Problem statement for a system with first-order differential equations. Updates the system differential variables. <br /></td></tr>
<tr class="separator:abaeae8f62a018d197f0187a1c80a90fe"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af3adf7b092a87868917ee5fb4255192b" id="r_af3adf7b092a87868917ee5fb4255192b"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#af3adf7b092a87868917ee5fb4255192b">exact_solution</a> (const double &amp;x, std::valarray&lt; double &gt; *y)</td></tr>
<tr class="memdesc:af3adf7b092a87868917ee5fb4255192b"><td class="mdescLeft">&#160;</td><td class="mdescRight">Exact solution of the problem. Used for solution comparison. <br /></td></tr>
<tr class="separator:af3adf7b092a87868917ee5fb4255192b"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga827bf009831ddc477c5fa8891d5cb35f" id="r_ga827bf009831ddc477c5fa8891d5cb35f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a> (const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</td></tr>
<tr class="memdesc:ga827bf009831ddc477c5fa8891d5cb35f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the semi-implicit-Euler method. <br /></td></tr>
<tr class="separator:ga827bf009831ddc477c5fa8891d5cb35f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga3874d294ab00fe9ce8731c5b7991a089" id="r_ga3874d294ab00fe9ce8731c5b7991a089"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_euler</a> (double dx, double x0, double x_max, std::valarray&lt; double &gt; *y, bool save_to_file=false)</td></tr>
<tr class="memdesc:ga3874d294ab00fe9ce8731c5b7991a089"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the semi-implicit-Euler method in the given limits. <br /></td></tr>
<tr class="separator:ga3874d294ab00fe9ce8731c5b7991a089"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<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/Semi-implicit_Euler_method" target="_blank">semi implicit 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">
@@ -176,14 +160,14 @@ Functions</h2></td></tr>
v(x) &amp;=&amp; -\sin(x)\\
\end{eqnarray*}
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<p> The computation results are stored to a text file <code>semi_implicit_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_semi_implicit_euler.svg" alt="Implementation solution" style="pointer-events: none;" class="inline"/></p>
<p> The computation results are stored to a text file <span class="tt">semi_implicit_euler.csv</span> and the exact soltuion results in <span class="tt">exact.csv</span> for comparison. <img src="https://raw.githubusercontent.com/TheAlgorithms/C-Plus-Plus/docs/images/numerical_methods/ode_semi_implicit_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="#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>
<div class="line">dy[0] = y[1];</div>
<div class="line">dy[1] = mu * (1.f - y[0] * y[0]) * y[1] - y[0];</div>
</div><!-- fragment --> <dl class="section see"><dt>See also</dt><dd><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using midpoint Euler method">ode_midpoint_euler.cpp</a>, <a class="el" href="../../db/dd3/ode__forward__euler_8cpp.html" title="Solve a multivariable first order ordinary differential equation (ODEs) using forward Euler method">ode_forward_euler.cpp</a> </dd></dl>
<p class="definition">Definition in file <a class="el" href="../../d3/d06/ode__semi__implicit__euler_8cpp_source.html">ode_semi_implicit_euler.cpp</a>.</p>
</div><h2 class="groupheader">Function Documentation</h2>
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<a id="af3adf7b092a87868917ee5fb4255192b" name="af3adf7b092a87868917ee5fb4255192b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af3adf7b092a87868917ee5fb4255192b">&#9670;&#160;</a></span>exact_solution()</h2>
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