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realstealthninja
2025-05-19 11:38:33 +00:00
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d6/dd3/ode__midpoint__euler_8cpp_source.html
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@@ -4,7 +4,7 @@
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
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<title>TheAlgorithms/C++: numerical_methods/ode_midpoint_euler.cpp Source File</title>
<link rel="icon" href="../../favicon.svg" type="image/x-icon" />
@@ -60,7 +60,7 @@ window.MathJax = {
</table>
</div>
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<!-- Generated by Doxygen 1.12.0 -->
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@@ -124,13 +124,14 @@ $(function(){initNavTree('d6/dd3/ode__midpoint__euler_8cpp_source.html','../../'
<div class="headertitle"><div class="title">ode_midpoint_euler.cpp</div></div>
</div><!--header-->
<div class="contents">
<a href="../../d6/dd3/ode__midpoint__euler_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<a href="../../d6/dd3/ode__midpoint__euler_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="preprocessor">#include &lt;ctime&gt;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor">#include &lt;fstream&gt;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor">#include &lt;valarray&gt;</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span></div>
<div class="foldopen" id="foldopen00053" data-start="{" data-end="}">
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"><a class="line" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe"> 53</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#abaeae8f62a018d197f0187a1c80a90fe">problem</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> &amp;x, std::valarray&lt;double&gt; *y,</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> std::valarray&lt;double&gt; *dy) {</div>
@@ -139,14 +140,14 @@ $(function(){initNavTree('d6/dd3/ode__midpoint__euler_8cpp_source.html','../../'
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> dy[0][1] = -omega * omega * y[0][0]; <span class="comment">// y dot</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span>}</div>
</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span></div>
<div class="foldopen" id="foldopen00066" data-start="{" data-end="}">
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"><a class="line" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b"> 66</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#af3adf7b092a87868917ee5fb4255192b">exact_solution</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> &amp;x, std::valarray&lt;double&gt; *y) {</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> y[0][0] = std::cos(x);</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> y[0][1] = -std::sin(x);</div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span>}</div>
</div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span></div>
<div class="foldopen" id="foldopen00085" data-start="{" data-end="}">
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"><a class="line" href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812"> 85</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/d60/group__ode.html#ga8c319db420c3d97a83e9dcca803b6812">midpoint_euler_step</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> dx, <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;x,</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> std::valarray&lt;double&gt; *y, std::valarray&lt;double&gt; *dy) {</div>
@@ -160,7 +161,7 @@ $(function(){initNavTree('d6/dd3/ode__midpoint__euler_8cpp_source.html','../../'
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> y[0] += dy[0] * dx;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span>}</div>
</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> </div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span></div>
<div class="foldopen" id="foldopen00107" data-start="{" data-end="}">
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"><a class="line" href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985"> 107</a></span><span class="keywordtype">double</span> <a class="code hl_function" href="../../d6/d60/group__ode.html#ga36ff0710861ca39d957046c0b09b2985">midpoint_euler</a>(<span class="keywordtype">double</span> dx, <span class="keywordtype">double</span> x0, <span class="keywordtype">double</span> x_max,</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> std::valarray&lt;double&gt; *y, <span class="keywordtype">bool</span> save_to_file = <span class="keyword">false</span>) {</div>
@@ -201,7 +202,8 @@ $(function(){initNavTree('d6/dd3/ode__midpoint__euler_8cpp_source.html','../../'
<div class="line"><a id="l00143" name="l00143"></a><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"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span>}</div>
</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span></div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span></div>
<div class="foldopen" id="foldopen00156" data-start="{" data-end="}">
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"><a class="line" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f"> 156</a></span><span class="keywordtype">void</span> <a class="code hl_function" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#aa13517b8e5de1b75592052db7f7e237f">save_exact_solution</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> &amp;X0, <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;X_MAX,</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;step_size,</div>
@@ -236,7 +238,7 @@ $(function(){initNavTree('d6/dd3/ode__midpoint__euler_8cpp_source.html','../../'
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> fp.close();</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span>}</div>
</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> </div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span></div>
<div class="foldopen" id="foldopen00192" data-start="{" data-end="}">
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"><a class="line" href="../../d6/dd3/ode__midpoint__euler_8cpp.html#a0ddf1224851353fc92bfbff6f499fa97"> 192</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span> *argv[]) {</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keywordtype">double</span> X0 = 0.f; <span class="comment">/* initial value of x0 */</span></div>
@@ -274,7 +276,7 @@ $(function(){initNavTree('d6/dd3/ode__midpoint__euler_8cpp_source.html','../../'
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
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<li class="navelem"><a class="el" href="../../dir_9c6faab82c22511b50177aa2e38e2780.html">numerical_methods</a></li><li class="navelem"><a class="el" href="../../d6/dd3/ode__midpoint__euler_8cpp.html">ode_midpoint_euler.cpp</a></li>
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