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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 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="../../d6/d60/group__ode.html#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a> (const double dx, const double x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</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, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&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="../../d6/d60/group__ode.html#gae0509f8843e2bc42de2abbd00a14b7b9">forward_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</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, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&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="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a> (const double dx, const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</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, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&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>
<tr class="memitem:ga36ff0710861ca39d957046c0b09b2985" id="r_ga36ff0710861ca39d957046c0b09b2985"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">midpoint_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
<tr class="memitem:ga36ff0710861ca39d957046c0b09b2985" id="r_ga36ff0710861ca39d957046c0b09b2985"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ga36ff0710861ca39d957046c0b09b2985">midpoint_euler</a> (double dx, double x0, double x_max, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</td></tr>
<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="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a> (const double dx, const double &amp;x, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *dy)</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, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&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, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *y, bool save_to_file=false)</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, <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&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>
<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>
<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 id="gae0509f8843e2bc42de2abbd00a14b7b9" name="gae0509f8843e2bc42de2abbd00a14b7b9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gae0509f8843e2bc42de2abbd00a14b7b9">&#9670;&#160;</a></span>forward_euler()</h2>
@@ -136,37 +138,27 @@ Functions</h2></td></tr>
<tr>
<td class="memname">double forward_euler </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>dx</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>dx</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x0</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x0</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x_max</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x_max</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>y</em>, </td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>y</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">bool&#160;</td>
<td class="paramname"><em>save_to_file</em> = <code>false</code>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
<td class="paramtype">bool</td> <td class="paramname"><span class="paramname"><em>save_to_file</em><span class="paramdefsep"> = </span><span class="paramdefval">false</span></span>&#160;)</td>
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@@ -210,7 +202,7 @@ Functions</h2></td></tr>
<div class="line"><span class="lineno"> 127</span> fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>; <span class="comment">// NOLINT</span></div>
<div class="line"><span class="lineno"> 128</span> }</div>
<div class="line"><span class="lineno"> 129</span> </div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_function" href="../../d6/d60/group__ode.html#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a>(dx, x, y, &amp;dy); <span class="comment">// perform integration</span></div>
<div class="line"><span class="lineno"> 130</span> <a class="code hl_function" href="#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a>(dx, x, y, &amp;dy); <span class="comment">// perform integration</span></div>
<div class="line"><span class="lineno"> 131</span> x += dx; <span class="comment">// update step</span></div>
<div class="line"><span class="lineno"> 132</span> } <span class="keywordflow">while</span> (x &lt;= x_max); <span class="comment">// till upper limit of independent variable</span></div>
<div class="line"><span class="lineno"> 133</span> <span class="comment">/* end of integration */</span></div>
@@ -226,7 +218,7 @@ Functions</h2></td></tr>
<div class="ttc" id="aclock_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock.html">std::clock</a></div><div class="ttdeci">T clock(T... args)</div></div>
<div class="ttc" id="aclock_t_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/chrono/c/clock_t.html">std::clock_t</a></div></div>
<div class="ttc" id="aclose_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/close.html">std::ofstream::close</a></div><div class="ttdeci">T close(T... args)</div></div>
<div class="ttc" id="agroup__ode_html_ga195d23bbdfcb80e83c9cda45c9ad5723"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a></div><div class="ttdeci">void forward_euler_step(const double dx, const double x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the forward-Euler method.</div><div class="ttdef"><b>Definition</b> ode_forward_euler.cpp:86</div></div>
<div class="ttc" id="agroup__ode_html_ga195d23bbdfcb80e83c9cda45c9ad5723"><div class="ttname"><a href="#ga195d23bbdfcb80e83c9cda45c9ad5723">forward_euler_step</a></div><div class="ttdeci">void forward_euler_step(const double dx, const double x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the forward-Euler method.</div><div class="ttdef"><b>Definition</b> ode_forward_euler.cpp:86</div></div>
<div class="ttc" id="ais_open_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/is_open.html">std::ofstream::is_open</a></div><div class="ttdeci">T is_open(T... args)</div></div>
<div class="ttc" id="aopen_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ofstream/open.html">std::ofstream::open</a></div><div class="ttdeci">T open(T... args)</div></div>
<div class="ttc" id="aperror_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/c/perror.html">std::perror</a></div><div class="ttdeci">T perror(T... args)</div></div>
@@ -249,31 +241,22 @@ Here is the call graph for this function:</div>
<tr>
<td class="memname">void forward_euler_step </td>
<td>(</td>
<td class="paramtype">const double&#160;</td>
<td class="paramname"><em>dx</em>, </td>
<td class="paramtype">const double</td> <td class="paramname"><span class="paramname"><em>dx</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double&#160;</td>
<td class="paramname"><em>x</em>, </td>
<td class="paramtype">const double</td> <td class="paramname"><span class="paramname"><em>x</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>y</em>, </td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>y</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>dy</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>dy</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
@@ -313,37 +296,27 @@ Here is the call graph for this function:</div>
<tr>
<td class="memname">double midpoint_euler </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>dx</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>dx</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x0</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x0</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x_max</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x_max</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>y</em>, </td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>y</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">bool&#160;</td>
<td class="paramname"><em>save_to_file</em> = <code>false</code>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
<td class="paramtype">bool</td> <td class="paramname"><span class="paramname"><em>save_to_file</em><span class="paramdefsep"> = </span><span class="paramdefval">false</span></span>&#160;)</td>
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@@ -386,7 +359,7 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 131</span> fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 132</span> }</div>
<div class="line"><span class="lineno"> 133</span> </div>
<div class="line"><span class="lineno"> 134</span> <a class="code hl_function" href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a>(dx, x, y, &amp;dy); <span class="comment">// perform integration</span></div>
<div class="line"><span class="lineno"> 134</span> <a class="code hl_function" href="#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a>(dx, x, y, &amp;dy); <span class="comment">// perform integration</span></div>
<div class="line"><span class="lineno"> 135</span> x += dx; <span class="comment">// update step</span></div>
<div class="line"><span class="lineno"> 136</span> } <span class="keywordflow">while</span> (x &lt;= x_max); <span class="comment">// till upper limit of independent variable</span></div>
<div class="line"><span class="lineno"> 137</span> <span class="comment">/* end of integration */</span></div>
@@ -397,7 +370,7 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 142</span> </div>
<div class="line"><span class="lineno"> 143</span> <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
<div class="line"><span class="lineno"> 144</span>}</div>
<div class="ttc" id="agroup__ode_html_ga8c319db420c3d97a83e9dcca803b6812"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a></div><div class="ttdeci">void midpoint_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the midpoint-Euler method.</div><div class="ttdef"><b>Definition</b> ode_midpoint_euler.cpp:85</div></div>
<div class="ttc" id="agroup__ode_html_ga8c319db420c3d97a83e9dcca803b6812"><div class="ttname"><a href="#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a></div><div class="ttdeci">void midpoint_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the midpoint-Euler method.</div><div class="ttdef"><b>Definition</b> ode_midpoint_euler.cpp:85</div></div>
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<tr>
<td class="memname">void midpoint_euler_step </td>
<td>(</td>
<td class="paramtype">const double&#160;</td>
<td class="paramname"><em>dx</em>, </td>
<td class="paramtype">const double</td> <td class="paramname"><span class="paramname"><em>dx</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double &amp;&#160;</td>
<td class="paramname"><em>x</em>, </td>
<td class="paramtype">const double &amp;</td> <td class="paramname"><span class="paramname"><em>x</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>y</em>, </td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>y</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>dy</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>dy</em></span>&#160;)</td>
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<td class="memname">double semi_implicit_euler </td>
<td>(</td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>dx</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>dx</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x0</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x0</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>x_max</em>, </td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x_max</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>y</em>, </td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>y</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">bool&#160;</td>
<td class="paramname"><em>save_to_file</em> = <code>false</code>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
<td class="paramtype">bool</td> <td class="paramname"><span class="paramname"><em>save_to_file</em><span class="paramdefsep"> = </span><span class="paramdefval">false</span></span>&#160;)</td>
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@@ -559,7 +513,7 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 128</span> fp &lt;&lt; y[0][L - 1] &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 129</span> }</div>
<div class="line"><span class="lineno"> 130</span> </div>
<div class="line"><span class="lineno"> 131</span> <a class="code hl_function" href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a>(dx, x, y, &amp;dy); <span class="comment">// perform integration</span></div>
<div class="line"><span class="lineno"> 131</span> <a class="code hl_function" href="#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a>(dx, x, y, &amp;dy); <span class="comment">// perform integration</span></div>
<div class="line"><span class="lineno"> 132</span> x += dx; <span class="comment">// update step</span></div>
<div class="line"><span class="lineno"> 133</span> } <span class="keywordflow">while</span> (x &lt;= x_max); <span class="comment">// till upper limit of independent variable</span></div>
<div class="line"><span class="lineno"> 134</span> <span class="comment">/* end of integration */</span></div>
@@ -570,7 +524,7 @@ Here is the call graph for this function:</div>
<div class="line"><span class="lineno"> 139</span> </div>
<div class="line"><span class="lineno"> 140</span> <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">double</span><span class="keyword">&gt;</span>(t2 - t1) / CLOCKS_PER_SEC;</div>
<div class="line"><span class="lineno"> 141</span>}</div>
<div class="ttc" id="agroup__ode_html_ga827bf009831ddc477c5fa8891d5cb35f"><div class="ttname"><a href="../../d6/d60/group__ode.html#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a></div><div class="ttdeci">void semi_implicit_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the semi-implicit-Euler method.</div><div class="ttdef"><b>Definition</b> ode_semi_implicit_euler.cpp:82</div></div>
<div class="ttc" id="agroup__ode_html_ga827bf009831ddc477c5fa8891d5cb35f"><div class="ttname"><a href="#ga827bf009831ddc477c5fa8891d5cb35f">semi_implicit_euler_step</a></div><div class="ttdeci">void semi_implicit_euler_step(const double dx, const double &amp;x, std::valarray&lt; double &gt; *y, std::valarray&lt; double &gt; *dy)</div><div class="ttdoc">Compute next step approximation using the semi-implicit-Euler method.</div><div class="ttdef"><b>Definition</b> ode_semi_implicit_euler.cpp:82</div></div>
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<td class="memname">void semi_implicit_euler_step </td>
<td>(</td>
<td class="paramtype">const double&#160;</td>
<td class="paramname"><em>dx</em>, </td>
<td class="paramtype">const double</td> <td class="paramname"><span class="paramname"><em>dx</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double &amp;&#160;</td>
<td class="paramname"><em>x</em>, </td>
<td class="paramtype">const double &amp;</td> <td class="paramname"><span class="paramname"><em>x</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>y</em>, </td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>y</em>, </span></td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *&#160;</td>
<td class="paramname"><em>dy</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/valarray.html">std::valarray</a>&lt; double &gt; *</td> <td class="paramname"><span class="paramname"><em>dy</em></span>&#160;)</td>
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