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<p><a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_blank">Runge Kutta fourth order</a> method implementation
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
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Include dependency graph for rungekutta.cpp:</div>
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<p><a href="../../d1/da6/rungekutta_8cpp_source.html">Go to the source code of this file.</a></p>
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Namespaces</h2></td></tr>
<tr class="memitem:numerical_5Fmethods" id="r_numerical_5Fmethods"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/de0/namespacenumerical__methods.html">numerical_methods</a></td></tr>
<tr class="memdesc:d1/de0/namespacenumerical__methods"><td class="mdescLeft">&#160;</td><td class="mdescRight">for assert <br /></td></tr>
<tr class="memitem:runge_5Fkutta" id="r_runge_5Fkutta"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/de7/namespacerunge__kutta.html">runge_kutta</a></td></tr>
<tr class="memdesc:d2/de7/namespacerunge__kutta"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_blank">Runge Kutta fourth order</a> method. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a7b9f40c7b5e9749cc550f19be3dc8856" id="r_a7b9f40c7b5e9749cc550f19be3dc8856"><td class="memItemLeft" align="right" valign="top">double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a> (double init_x, const double &amp;init_y, const double &amp;x, const double &amp;<a class="el" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>)</td></tr>
<tr class="memdesc:a7b9f40c7b5e9749cc550f19be3dc8856"><td class="mdescLeft">&#160;</td><td class="mdescRight">the Runge Kutta method finds the value of integration of a function in the given limits. the lower limit of integration as the initial value and the upper limit is the given x <br /></td></tr>
<tr id="func-members-0" class="groupHeader"><td colspan="2"><div class="groupHeader"></div></td></tr>
<tr class="memitem:a450497475f5607333f9aca8f88901579" id="r_a450497475f5607333f9aca8f88901579"><td class="memItemLeft" align="right" valign="top">static double&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#a450497475f5607333f9aca8f88901579">change</a> (double x, double y)</td></tr>
<tr class="memdesc:a450497475f5607333f9aca8f88901579"><td class="mdescLeft">&#160;</td><td class="mdescRight">asserting the test functions <br /></td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Tests to check algorithm implementation. <br /></td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
</table>
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_blank">Runge Kutta fourth order</a> method implementation </p>
<dl class="section author"><dt>Author</dt><dd><a href="http://github.com/rudra697" target="_blank">Rudra Prasad Das</a></dd></dl>
<p>It solves the unknown value of y for a given value of x only first order differential equations can be solved </p>
<p class="definition">Definition in file <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html">rungekutta.cpp</a>.</p>
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
<a id="a450497475f5607333f9aca8f88901579" name="a450497475f5607333f9aca8f88901579"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a450497475f5607333f9aca8f88901579">&#9670;&#160;</a></span>change()</h2>
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<td class="memname">double change </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>x</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>y</em></span>&#160;)</td>
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</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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<p>asserting the test functions </p>
<p>for io operations for using the vector container</p>
<p>The <a class="el" href="#a450497475f5607333f9aca8f88901579" title="asserting the test functions">change()</a> function is used to return the updated iterative value corresponding to the given function </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>is the value corresponding to the x coordinate </td></tr>
<tr><td class="paramname">y</td><td>is the value corresponding to the y coordinate </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the computed function value at that call </dd></dl>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a0">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>.</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html#l00033">33</a> of file <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html">rungekutta.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 33</span>{ <span class="keywordflow">return</span> ((x - y) / 2.0); }</div>
</div><!-- fragment -->
</div>
</div>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
<td></td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html#l00130">130</a> of file <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html">rungekutta.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 130</span> {</div>
<div class="line"><span class="lineno"> 131</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Execute the tests</span></div>
<div class="line"><span class="lineno"> 132</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 133</span>}</div>
<div class="ttc" id="arungekutta_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Tests to check algorithm implementation.</div><div class="ttdef"><b>Definition</b> <a href="../../d1/da6/rungekutta_8cpp_source.html#l00100">rungekutta.cpp:100</a></div></div>
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<a id="a7b9f40c7b5e9749cc550f19be3dc8856" name="a7b9f40c7b5e9749cc550f19be3dc8856"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a7b9f40c7b5e9749cc550f19be3dc8856">&#9670;&#160;</a></span>rungeKutta()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">double numerical_methods::runge_kutta::rungeKutta </td>
<td>(</td>
<td class="paramtype">double</td> <td class="paramname"><span class="paramname"><em>init_x</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">const double &amp;</td> <td class="paramname"><span class="paramname"><em>init_y</em></span>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></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">const double &amp;</td> <td class="paramname"><span class="paramname"><em>h</em></span>&#160;)</td>
</tr>
</table>
</div><div class="memdoc">
<p>the Runge Kutta method finds the value of integration of a function in the given limits. the lower limit of integration as the initial value and the upper limit is the given x </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">init_x</td><td>is the value of initial x and is updated after each call </td></tr>
<tr><td class="paramname">init_y</td><td>is the value of initial x and is updated after each call </td></tr>
<tr><td class="paramname">x</td><td>is current iteration at which the function needs to be evaluated </td></tr>
<tr><td class="paramname">h</td><td>is the step value </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>the value of y at thr required value of x from the initial conditions </dd></dl>
<dl class="section examples"><dt>Examples</dt><dd><a class="el" href="../../dc/dc4/_2_users_2runner_2work_2_c-_plus-_plus_2_c-_plus-_plus_2numerical_methods_2rungekutta_8cpp-example.html#a1">/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp</a>.</dd>
</dl>
<p class="definition">Definition at line <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html#l00057">57</a> of file <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html">rungekutta.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 58</span> {</div>
<div class="line"><span class="lineno"> 59</span> <span class="comment">// Count number of iterations</span></div>
<div class="line"><span class="lineno"> 60</span> <span class="comment">// using step size or</span></div>
<div class="line"><span class="lineno"> 61</span> <span class="comment">// step height h</span></div>
<div class="line"><span class="lineno"> 62</span> </div>
<div class="line"><span class="lineno"> 63</span> <span class="comment">// n calucates the number of iterations</span></div>
<div class="line"><span class="lineno"> 64</span> <span class="comment">// k1, k2, k3, k4 are the Runge Kutta variables</span></div>
<div class="line"><span class="lineno"> 65</span> <span class="comment">// used for calculation of y at each iteration</span></div>
<div class="line"><span class="lineno"> 66</span> </div>
<div class="line"><span class="lineno"> 67</span> <span class="keyword">auto</span> n = <span class="keyword">static_cast&lt;</span>uint64_t<span class="keyword">&gt;</span>((x - init_x) / <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>);</div>
<div class="line"><span class="lineno"> 68</span> <span class="comment">// used a vector container for the variables</span></div>
<div class="line"><span class="lineno"> 69</span> std::vector&lt;double&gt; k(4, 0.0);</div>
<div class="line"><span class="lineno"> 70</span> </div>
<div class="line"><span class="lineno"> 71</span> <span class="comment">// Iterate for number of iterations</span></div>
<div class="line"><span class="lineno"> 72</span> </div>
<div class="line"><span class="lineno"> 73</span> <span class="keywordtype">double</span> y = init_y;</div>
<div class="line"><span class="lineno"> 74</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= n; ++i) {</div>
<div class="line"><span class="lineno"> 75</span> <span class="comment">// Apply Runge Kutta Formulas</span></div>
<div class="line"><span class="lineno"> 76</span> <span class="comment">// to find next value of y</span></div>
<div class="line"><span class="lineno"> 77</span> k[0] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="#a450497475f5607333f9aca8f88901579">change</a>(init_x, y);</div>
<div class="line"><span class="lineno"> 78</span> k[1] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5 * <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5 * k[0]);</div>
<div class="line"><span class="lineno"> 79</span> k[2] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="#a450497475f5607333f9aca8f88901579">change</a>(init_x + 0.5 * <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + 0.5 * k[1]);</div>
<div class="line"><span class="lineno"> 80</span> k[3] = <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a> * <a class="code hl_function" href="#a450497475f5607333f9aca8f88901579">change</a>(init_x + <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>, y + k[2]);</div>
<div class="line"><span class="lineno"> 81</span> </div>
<div class="line"><span class="lineno"> 82</span> <span class="comment">// Update next value of y</span></div>
<div class="line"><span class="lineno"> 83</span> </div>
<div class="line"><span class="lineno"> 84</span> y += (1.0 / 6.0) * (k[0] + 2 * k[1] + 2 * k[2] + k[3]);</div>
<div class="line"><span class="lineno"> 85</span> </div>
<div class="line"><span class="lineno"> 86</span> <span class="comment">// Update next value of x</span></div>
<div class="line"><span class="lineno"> 87</span> </div>
<div class="line"><span class="lineno"> 88</span> init_x += <a class="code hl_function" href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a>;</div>
<div class="line"><span class="lineno"> 89</span> }</div>
<div class="line"><span class="lineno"> 90</span> </div>
<div class="line"><span class="lineno"> 91</span> <span class="keywordflow">return</span> y;</div>
<div class="line"><span class="lineno"> 92</span>}</div>
<div class="ttc" id="ahash__search_8cpp_html_a566eaf0ffafd50bc61e644561fd27001"><div class="ttname"><a href="../../d1/df3/hash__search_8cpp.html#a566eaf0ffafd50bc61e644561fd27001">h</a></div><div class="ttdeci">int h(int key)</div><div class="ttdef"><b>Definition</b> <a href="../../d1/df3/hash__search_8cpp_source.html#l00045">hash_search.cpp:45</a></div></div>
<div class="ttc" id="arungekutta_8cpp_html_a450497475f5607333f9aca8f88901579"><div class="ttname"><a href="#a450497475f5607333f9aca8f88901579">change</a></div><div class="ttdeci">static double change(double x, double y)</div><div class="ttdoc">asserting the test functions</div><div class="ttdef"><b>Definition</b> <a href="../../d1/da6/rungekutta_8cpp_source.html#l00033">rungekutta.cpp:33</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">void test </td>
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<p>Tests to check algorithm implementation. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<p class="definition">Definition at line <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html#l00100">100</a> of file <a class="el" href="../../d1/da6/rungekutta_8cpp_source.html">rungekutta.cpp</a>.</p>
<div class="fragment"><div class="line"><span class="lineno"> 100</span> {</div>
<div class="line"><span class="lineno"> 101</span> std::cout &lt;&lt; <span class="stringliteral">&quot;The Runge Kutta function will be tested on the basis of &quot;</span></div>
<div class="line"><span class="lineno"> 102</span> <span class="stringliteral">&quot;precomputed values\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 103</span> </div>
<div class="line"><span class="lineno"> 104</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 1....&quot;</span></div>
<div class="line"><span class="lineno"> 105</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 106</span> <span class="keywordtype">double</span> valfirst = <a class="code hl_function" href="#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(</div>
<div class="line"><span class="lineno"> 107</span> 2, 3, 4, 0.2); <span class="comment">// Tests the function with pre calculated values</span></div>
<div class="line"><span class="lineno"> 108</span> assert(valfirst == 3.10363932323749570);</div>
<div class="line"><span class="lineno"> 109</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 1\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 110</span> </div>
<div class="line"><span class="lineno"> 111</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 2....&quot;</span></div>
<div class="line"><span class="lineno"> 112</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 113</span> <span class="keywordtype">double</span> valsec = <a class="code hl_function" href="#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(</div>
<div class="line"><span class="lineno"> 114</span> 1, 2, 5, 0.1); <span class="comment">// The value of step changed</span></div>
<div class="line"><span class="lineno"> 115</span> assert(valsec == 3.40600589380261409);</div>
<div class="line"><span class="lineno"> 116</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 2\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 117</span> </div>
<div class="line"><span class="lineno"> 118</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Test 3....&quot;</span></div>
<div class="line"><span class="lineno"> 119</span> &lt;&lt; <span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 120</span> <span class="keywordtype">double</span> valthird = <a class="code hl_function" href="#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a>(</div>
<div class="line"><span class="lineno"> 121</span> -1, 3, 4, 0.1); <span class="comment">// Tested with negative value</span></div>
<div class="line"><span class="lineno"> 122</span> assert(valthird == 2.49251005860244268);</div>
<div class="line"><span class="lineno"> 123</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Passed Test 3\n&quot;</span>;</div>
<div class="line"><span class="lineno"> 124</span>}</div>
<div class="ttc" id="arungekutta_8cpp_html_a7b9f40c7b5e9749cc550f19be3dc8856"><div class="ttname"><a href="#a7b9f40c7b5e9749cc550f19be3dc8856">numerical_methods::runge_kutta::rungeKutta</a></div><div class="ttdeci">double rungeKutta(double init_x, const double &amp;init_y, const double &amp;x, const double &amp;h)</div><div class="ttdoc">the Runge Kutta method finds the value of integration of a function in the given limits....</div><div class="ttdef"><b>Definition</b> <a href="../../d1/da6/rungekutta_8cpp_source.html#l00057">rungekutta.cpp:57</a></div></div>
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