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Include dependency graph for ode_semi_implicit_euler.cpp:</div>
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@@ -131,8 +138,8 @@ Functions</h2></td></tr>
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<a name="details" id="details"></a><h2 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">
<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\\
@@ -140,7 +147,7 @@ Functions</h2></td></tr>
[x_0, u_0, v_0] &amp;=&amp; [0,1,0]\qquad\ldots\text{(initial values)}
\end{eqnarray*}
</p>
<p> The exact solution for the above problem is: </p><p class="formulaDsp">
<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)\\
@@ -153,7 +160,7 @@ v(x) &amp;=&amp; -\sin(x)\\
</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>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="af3adf7b092a87868917ee5fb4255192b" name="af3adf7b092a87868917ee5fb4255192b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#af3adf7b092a87868917ee5fb4255192b">&#9670;&nbsp;</a></span>exact_solution()</h2>
<h2 class="memtitle"><span class="permalink"><a href="#af3adf7b092a87868917ee5fb4255192b">&#9670;&#160;</a></span>exact_solution()</h2>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="agroup__ode_html_ga3874d294ab00fe9ce8731c5b7991a089"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga3874d294ab00fe9ce8731c5b7991a089">semi_implicit_euler</a></div><div class="ttdeci">double semi_implicit_euler(double dx, double x0, double x_max, std::valarray&lt; double &gt; *y, bool save_to_file=false)</div><div class="ttdoc">Compute approximation using the semi-implicit-Euler method in the given limits.</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:103</div></div>
<div class="ttc" id="aode__semi__implicit__euler_8cpp_html_aa13517b8e5de1b75592052db7f7e237f"><div class="ttname"><a href="../../d3/d06/ode__semi__implicit__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a></div><div class="ttdeci">void save_exact_solution(const double &amp;X0, const double &amp;X_MAX, const double &amp;step_size, const std::valarray&lt; double &gt; &amp;Y0)</div><div class="ttdef"><b>Definition:</b> ode_semi_implicit_euler.cpp:153</div></div>
<div class="ttc" id="avalarray_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray&lt; double &gt;</a></div></div>
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