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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.runge_kutta_fehlberg78"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template runge_kutta_fehlberg78</span></h2>
  29 <p>boost::numeric::odeint::runge_kutta_fehlberg78 &#8212; The Runge-Kutta Fehlberg 78 method. </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_kutta_fehlberg78_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp&gt;">boost/numeric/odeint/stepper/runge_kutta_fehlberg78.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_kutta_fehlberg78.html" title="Class template runge_kutta_fehlberg78">runge_kutta_fehlberg78</a> <span class="special">:</span> <span class="keyword">public</span> boost::numeric::odeint::explicit_error_generic_rk&lt; StageCount, Order, StepperOrder, ErrorOrder, 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_kutta_fehlberg78.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_kutta_fehlberg78.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_kutta_fehlberg78.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_kutta_fehlberg78.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_kutta_fehlberg78.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_kutta_fehlberg78.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_kutta_fehlberg78.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  50
  51   <span class="comment">// <a class="link" href="runge_kutta_fehlberg78.html#boost.numeric.odeint.runge_kutta_fehlberg78construct-copy-destruct">construct/copy/destruct</a></span>
  52   <a class="link" href="runge_kutta_fehlberg78.html#idp32918720-bb"><span class="identifier">runge_kutta_fehlberg78</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_kutta_fehlberg78.html#idp32898128-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">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
  57     <span class="keyword">void</span> <a class="link" href="runge_kutta_fehlberg78.html#idp32898688-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="identifier">Err</span> <span class="special">&amp;</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> 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>
  60            <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
  61     <span class="keyword">void</span> <a class="link" href="runge_kutta_fehlberg78.html#idp32907440-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>
  62                       <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>
  63   <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_kutta_fehlberg78.html#idp32914944-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>
  64 <span class="special">}</span><span class="special">;</span></pre></div>
  65 <div class="refsect1">
  66 <a name="idp115111824"></a><h2>Description</h2>
  67 <p>The Runge-Kutta Fehlberg 78 method is a standard method for high-precision applications. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.</p>
  68 <p>This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from <a class="link" href="explicit_error_generic_rk.html" title="Class template explicit_error_generic_rk">explicit_error_generic_rk</a> which is a generic Runge-Kutta algorithm with error estimation. For more details see explicit_error_stepper_base and <a class="link" href="explicit_error_generic_rk.html" title="Class template explicit_error_generic_rk">explicit_error_generic_rk</a>.</p>
  69 <p>
  70 </p>
  71 <div class="refsect2">
  72 <a name="idp115115392"></a><h3>Template Parameters</h3>
  73 <div class="orderedlist"><ol class="orderedlist" type="1">
  74 <li class="listitem">
  75 <pre class="literallayout"><span class="keyword">typename</span> State</pre>
  76 <p>The state type. </p>
  77 </li>
  78 <li class="listitem">
  79 <pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre>
  80 <p>The value type. </p>
  81 </li>
  82 <li class="listitem">
  83 <pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre>
  84 <p>The type representing the time derivative of the state. </p>
  85 </li>
  86 <li class="listitem">
  87 <pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre>
  88 <p>The time representing the independent variable - the time. </p>
  89 </li>
  90 <li class="listitem">
  91 <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>
  92 <p>The algebra type. </p>
  93 </li>
  94 <li class="listitem">
  95 <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>
  96 <p>The operations type. </p>
  97 </li>
  98 <li class="listitem">
  99 <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre>
 100 <p>The resizer policy type. </p>
 101 </li>
 102 </ol></div>
 103 </div>
 104 <div class="refsect2">
 105 <a name="idp115145680"></a><h3>
 106 <a name="boost.numeric.odeint.runge_kutta_fehlberg78construct-copy-destruct"></a><code class="computeroutput">runge_kutta_fehlberg78</code>
 107         public
 108        construct/copy/destruct</h3>
 109 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
 110 <pre class="literallayout"><a name="idp32918720-bb"></a><span class="identifier">runge_kutta_fehlberg78</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 runge_kutta_cash_fehlberg78 class. This constructor can be used as a default constructor if the algebra has a default constructor. <p>
 111 </p>
 112 <div class="variablelist"><table border="0" class="variablelist compact">
 113 <colgroup>
 114 <col align="left" valign="top">
 115 <col>
 116 </colgroup>
 117 <tbody><tr>
 118 <td><p><span class="term">Parameters:</span></p></td>
 119 <td><div class="variablelist"><table border="0" class="variablelist compact">
 120 <colgroup>
 121 <col align="left" valign="top">
 122 <col>
 123 </colgroup>
 124 <tbody><tr>
 125 <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td>
 126 <td><p>A copy of algebra is made and stored inside explicit_stepper_base. </p></td>
 127 </tr></tbody>
 128 </table></div></td>
 129 </tr></tbody>
 130 </table></div>
 131 </li></ol></div>
 132 </div>
 133 <div class="refsect2">
 134 <a name="idp115159504"></a><h3>
 135 <a name="idp32898128-bb"></a><code class="computeroutput">runge_kutta_fehlberg78</code> public member functions</h3>
 136 <div class="orderedlist"><ol class="orderedlist" type="1">
 137 <li class="listitem"><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>
 138          <span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
 139   <span class="keyword">void</span> <a name="idp32898688-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>
 140                     <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="identifier">Err</span> <span class="special">&amp;</span> xerr<span class="special">)</span><span class="special">;</span></pre></li>
 141 <li class="listitem"><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>
 142          <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
 143   <span class="keyword">void</span> <a name="idp32907440-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>
 144                     <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></li>
 145 <li class="listitem">
 146 <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="idp32914944-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>
 147 </p>
 148 <div class="variablelist"><table border="0" class="variablelist compact">
 149 <colgroup>
 150 <col align="left" valign="top">
 151 <col>
 152 </colgroup>
 153 <tbody><tr>
 154 <td><p><span class="term">Parameters:</span></p></td>
 155 <td><div class="variablelist"><table border="0" class="variablelist compact">
 156 <colgroup>
 157 <col align="left" valign="top">
 158 <col>
 159 </colgroup>
 160 <tbody><tr>
 161 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 162 <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td>
 163 </tr></tbody>
 164 </table></div></td>
 165 </tr></tbody>
 166 </table></div>
 167 </li>
 168 </ol></div>
 169 </div>
 170 </div>
 171 </div>
 172 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 173 <td align="left"></td>
 174 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2012 Karsten
 175       Ahnert and Mario Mulansky<p>
 176         Distributed under the Boost Software License, Version 1.0. (See accompanying
 177         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>)
 178       </p>
 179 </div></td>
 180 </tr></table>
 181 <hr>
 182 <div class="spirit-nav">
 183 <a accesskey="p" href="../../../header/boost/numeric/odeint/stepper/runge_kutta_fehlberg78_hpp.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../header/boost/numeric/odeint/stepper/runge_kutta_fehlberg78_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/stepper_categories_hpp.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
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