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<title>TheAlgorithms/C++: Ordinary Differential Equations</title>
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<div class="header">
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<a href="#func-members">Functions</a> </div>
<div class="headertitle"><div class="title">Ordinary Differential Equations</div></div>
<div class="headertitle"><div class="title">Ordinary Differential Equations </div></div>
</div><!--header-->
<div class="contents">
<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:ga195d23bbdfcb80e83c9cda45c9ad5723" id="r_ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a> (const double dx, const double x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</td></tr>
<tr class="memdesc:ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the forward-Euler method. <br /></td></tr>
<tr class="separator:ga195d23bbdfcb80e83c9cda45c9ad5723"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:gae0509f8843e2bc42de2abbd00a14b7b9" id="r_gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#gae0509f8843e2bc42de2abbd00a14b7b9">forward_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:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the forward-Euler method in the given limits. <br /></td></tr>
<tr class="separator:gae0509f8843e2bc42de2abbd00a14b7b9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ga8c319db420c3d97a83e9dcca803b6812" id="r_ga8c319db420c3d97a83e9dcca803b6812"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ga8c319db420c3d97a83e9dcca803b6812">midpoint_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:ga8c319db420c3d97a83e9dcca803b6812"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute next step approximation using the midpoint-Euler method. <br /></td></tr>
<tr class="separator:ga8c319db420c3d97a83e9dcca803b6812"><td class="memSeparator" colspan="2">&#160;</td></tr>
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<tr class="memdesc:ga36ff0710861ca39d957046c0b09b2985"><td class="mdescLeft">&#160;</td><td class="mdescRight">Compute approximation using the midpoint-Euler method in the given limits. <br /></td></tr>
<tr class="separator:ga36ff0710861ca39d957046c0b09b2985"><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="#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="#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>
<p>Integration functions for implementations with solving <a href="https://en.wikipedia.org/wiki/Ordinary_differential_equation" target="_blank">ordinary differential equations</a> (ODEs) of any order and and any number of independent variables.</p>
<h2 class="groupheader">Function Documentation</h2>
<a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="gae0509f8843e2bc42de2abbd00a14b7b9" name="gae0509f8843e2bc42de2abbd00a14b7b9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gae0509f8843e2bc42de2abbd00a14b7b9">&#9670;&#160;</a></span>forward_euler()</h2>
@@ -589,10 +573,18 @@ y_n + \frac{1}{2}dx\,f\left(x_n,y_n\right)\right)\]
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