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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.runge_kutta4"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template runge_kutta4</span></h2>
  29 <p>boost::numeric::odeint::runge_kutta4 &#8212; The classical Runge-Kutta stepper of fourth order. </p>
  30 </div>
  31 <h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
  32 <div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: &lt;<a class="link" href="../../../header/boost/numeric/odeint/stepper/runge_kutta4_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/runge_kutta4.hpp&gt;">boost/numeric/odeint/stepper/runge_kutta4.hpp</a>&gt;
  33
  34 </span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> State<span class="special">,</span> <span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> <span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span><span class="special">,</span>
  35          <span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span><span class="special">,</span>
  36          <span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">algebra_type</span><span class="special">,</span>
  37          <span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">operations_type</span><span class="special">,</span>
  38          <span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span><span class="special">&gt;</span>
  39 <span class="keyword">class</span> <a class="link" href="runge_kutta4.html" title="Class template runge_kutta4">runge_kutta4</a> <span class="special">:</span> <span class="keyword">public</span> boost::numeric::odeint::explicit_generic_rk&lt; StageCount, Order, State, Value, Deriv, Time, Algebra, Operations, Resizer &gt;
  40 <span class="special">{</span>
  41 <span class="keyword">public</span><span class="special">:</span>
  42   <span class="comment">// types</span>
  43   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">state_type</span>      <a name="boost.numeric.odeint.runge_kutta4.state_type"></a><span class="identifier">state_type</span><span class="special">;</span>
  44   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">value_type</span>      <a name="boost.numeric.odeint.runge_kutta4.value_type"></a><span class="identifier">value_type</span><span class="special">;</span>
  45   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">deriv_type</span>      <a name="boost.numeric.odeint.runge_kutta4.deriv_type"></a><span class="identifier">deriv_type</span><span class="special">;</span>
  46   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">time_type</span>       <a name="boost.numeric.odeint.runge_kutta4.time_type"></a><span class="identifier">time_type</span><span class="special">;</span>
  47   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">algebra_type</span>    <a name="boost.numeric.odeint.runge_kutta4.algebra_type"></a><span class="identifier">algebra_type</span><span class="special">;</span>
  48   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">operations_type</span> <a name="boost.numeric.odeint.runge_kutta4.operations_type"></a><span class="identifier">operations_type</span><span class="special">;</span>
  49   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">resizer_type</span>    <a name="boost.numeric.odeint.runge_kutta4.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  50
  51   <span class="comment">// <a class="link" href="runge_kutta4.html#boost.numeric.odeint.runge_kutta4construct-copy-destruct">construct/copy/destruct</a></span>
  52   <a class="link" href="runge_kutta4.html#idm45853738841952-bb"><span class="identifier">runge_kutta4</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</span> <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span>
  53
  54   <span class="comment">// <a class="link" href="runge_kutta4.html#idm45853738860096-bb">public member functions</a></span>
  55   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">,</span>
  56            <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
  57     <span class="keyword">void</span> <a class="link" href="runge_kutta4.html#idm45853738859536-bb"><span class="identifier">do_step_impl</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span>
  58                       <span class="identifier">StateOut</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  59   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="runge_kutta4.html#idm45853738845728-bb"><span class="identifier">adjust_size</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  60 <span class="special">}</span><span class="special">;</span></pre></div>
  61 <div class="refsect1">
  62 <a name="idm45221356587040"></a><h2>Description</h2>
  63 <p>The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also <a href="http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_top">en.wikipedia.org/wiki/Runge-Kutta_methods</a> The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.</p>
  64 <p>This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from <a class="link" href="explicit_generic_rk.html" title="Class template explicit_generic_rk">explicit_generic_rk</a> which is a generic Runge-Kutta algorithm. For more details see explicit_stepper_base and <a class="link" href="explicit_generic_rk.html" title="Class template explicit_generic_rk">explicit_generic_rk</a>.</p>
  65 <p>
  66 </p>
  67 <div class="refsect2">
  68 <a name="idm45221356582752"></a><h3>Template Parameters</h3>
  69 <div class="orderedlist"><ol class="orderedlist" type="1">
  70 <li class="listitem">
  71 <pre class="literallayout"><span class="keyword">typename</span> State</pre>
  72 <p>The state type. </p>
  73 </li>
  74 <li class="listitem">
  75 <pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre>
  76 <p>The value type. </p>
  77 </li>
  78 <li class="listitem">
  79 <pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre>
  80 <p>The type representing the time derivative of the state. </p>
  81 </li>
  82 <li class="listitem">
  83 <pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre>
  84 <p>The time representing the independent variable - the time. </p>
  85 </li>
  86 <li class="listitem">
  87 <pre class="literallayout"><span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">algebra_type</span></pre>
  88 <p>The algebra type. </p>
  89 </li>
  90 <li class="listitem">
  91 <pre class="literallayout"><span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">operations_type</span></pre>
  92 <p>The operations type. </p>
  93 </li>
  94 <li class="listitem">
  95 <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre>
  96 <p>The resizer policy type. </p>
  97 </li>
  98 </ol></div>
  99 </div>
 100 <div class="refsect2">
 101 <a name="idm45221356552384"></a><h3>
 102 <a name="boost.numeric.odeint.runge_kutta4construct-copy-destruct"></a><code class="computeroutput">runge_kutta4</code>
 103         public
 104        construct/copy/destruct</h3>
 105 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
 106 <pre class="literallayout"><a name="idm45853738841952-bb"></a><span class="identifier">runge_kutta4</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</span> algebra <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span></pre>Constructs the <code class="computeroutput"><a class="link" href="runge_kutta4.html" title="Class template runge_kutta4">runge_kutta4</a></code> class. This constructor can be used as a default constructor if the algebra has a default constructor. <p>
 107 </p>
 108 <div class="variablelist"><table border="0" class="variablelist compact">
 109 <colgroup>
 110 <col align="left" valign="top">
 111 <col>
 112 </colgroup>
 113 <tbody><tr>
 114 <td><p><span class="term">Parameters:</span></p></td>
 115 <td><div class="variablelist"><table border="0" class="variablelist compact">
 116 <colgroup>
 117 <col align="left" valign="top">
 118 <col>
 119 </colgroup>
 120 <tbody><tr>
 121 <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td>
 122 <td><p>A copy of algebra is made and stored inside explicit_stepper_base. </p></td>
 123 </tr></tbody>
 124 </table></div></td>
 125 </tr></tbody>
 126 </table></div>
 127 </li></ol></div>
 128 </div>
 129 <div class="refsect2">
 130 <a name="idm45221356537344"></a><h3>
 131 <a name="idm45853738860096-bb"></a><code class="computeroutput">runge_kutta4</code> public member functions</h3>
 132 <div class="orderedlist"><ol class="orderedlist" type="1">
 133 <li class="listitem">
 134 <pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">,</span>
 135          <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
 136   <span class="keyword">void</span> <a name="idm45853738859536-bb"></a><span class="identifier">do_step_impl</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&amp;</span> in<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&amp;</span> dxdt<span class="special">,</span>
 137                     <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">StateOut</span> <span class="special">&amp;</span> out<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>This method performs one step. The derivative <code class="computeroutput">dxdt</code> of <code class="computeroutput">in</code> at the time <code class="computeroutput">t</code> is passed to the method. The result is updated out of place, hence the input is in <code class="computeroutput">in</code> and the output in <code class="computeroutput">out</code>. Access to this step functionality is provided by explicit_stepper_base and <code class="computeroutput">do_step_impl</code> should not be called directly. <p>
 138 </p>
 139 <div class="variablelist"><table border="0" class="variablelist compact">
 140 <colgroup>
 141 <col align="left" valign="top">
 142 <col>
 143 </colgroup>
 144 <tbody><tr>
 145 <td><p><span class="term">Parameters:</span></p></td>
 146 <td><div class="variablelist"><table border="0" class="variablelist compact">
 147 <colgroup>
 148 <col align="left" valign="top">
 149 <col>
 150 </colgroup>
 151 <tbody>
 152 <tr>
 153 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 154 <td><p>The step size. </p></td>
 155 </tr>
 156 <tr>
 157 <td><p><span class="term"><code class="computeroutput">dxdt</code></span></p></td>
 158 <td><p>The derivative of x at t. </p></td>
 159 </tr>
 160 <tr>
 161 <td><p><span class="term"><code class="computeroutput">in</code></span></p></td>
 162 <td><p>The state of the ODE which should be solved. in is not modified in this method </p></td>
 163 </tr>
 164 <tr>
 165 <td><p><span class="term"><code class="computeroutput">out</code></span></p></td>
 166 <td><p>The result of the step is written in out. </p></td>
 167 </tr>
 168 <tr>
 169 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 170 <td><p>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </p></td>
 171 </tr>
 172 <tr>
 173 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 174 <td><p>The value of the time, at which the step should be performed. </p></td>
 175 </tr>
 176 </tbody>
 177 </table></div></td>
 178 </tr></tbody>
 179 </table></div>
 180 </li>
 181 <li class="listitem">
 182 <pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">void</span> <a name="idm45853738845728-bb"></a><span class="identifier">adjust_size</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&amp;</span> x<span class="special">)</span><span class="special">;</span></pre>Adjust the size of all temporaries in the stepper manually. <p>
 183 </p>
 184 <div class="variablelist"><table border="0" class="variablelist compact">
 185 <colgroup>
 186 <col align="left" valign="top">
 187 <col>
 188 </colgroup>
 189 <tbody><tr>
 190 <td><p><span class="term">Parameters:</span></p></td>
 191 <td><div class="variablelist"><table border="0" class="variablelist compact">
 192 <colgroup>
 193 <col align="left" valign="top">
 194 <col>
 195 </colgroup>
 196 <tbody><tr>
 197 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 198 <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td>
 199 </tr></tbody>
 200 </table></div></td>
 201 </tr></tbody>
 202 </table></div>
 203 </li>
 204 </ol></div>
 205 </div>
 206 </div>
 207 </div>
 208 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 209 <td align="left"></td>
 210 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2015 Karsten Ahnert and Mario Mulansky<p>
 211         Distributed under the Boost Software License, Version 1.0. (See accompanying
 212         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
 213       </p>
 214 </div></td>
 215 </tr></table>
 216 <hr>
 217 <div class="spirit-nav">
 218 <a accesskey="p" href="../../../header/boost/numeric/odeint/stepper/runge_kutta4_hpp.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../header/boost/numeric/odeint/stepper/runge_kutta4_hpp.html"><img src="../../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../../../header/boost/numeric/odeint/stepper/runge_kutta4_classic_hpp.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
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