<?xml version="1.0" encoding="UTF-8" ?>
<!DOCTYPE Runge-Kutta PUBLIC "-//spaceroots.org//DTD Runge-Kutta V1.2//EN"
                             "http://www.spaceroots.org/Runge-Kutta.dtd" >

<!-- $Id: DormandPrince54.xml,v 1.3 2004/05/23 17:41:52 luc Exp $ -->

<Runge-Kutta name="Dormand-Prince 5(4)" >

  <time-steps>
    <zero/>
    <rational> <p>1</p> <q> 5</q> </rational>
    <rational> <p>3</p> <q>10</q> </rational>
    <rational> <p>4</p> <q> 5</q> </rational>
    <rational> <p>8</p> <q> 9</q> </rational>
    <one/>
    <one/>
  </time-steps>

  <internal-weights>
    <row>
      <!-- empty first row -->
    </row>
    <row>
      <rational> <p>     1</p> <q>    5</q> </rational>
    </row>
    <row>
      <rational> <p>     3</p> <q>   40</q> </rational>
      <rational> <p>     9</p> <q>   40</q> </rational>
    </row>
    <row>
      <rational> <p>    44</p> <q>   45</q> </rational>
      <rational> <p>   -56</p> <q>   15</q> </rational>
      <rational> <p>    32</p> <q>    9</q> </rational>
    </row>
    <row>
      <rational> <p> 19372</p> <q> 6561</q> </rational>
      <rational> <p>-25360</p> <q> 2187</q> </rational>
      <rational> <p> 64448</p> <q> 6561</q> </rational>
      <rational> <p>  -212</p> <q>  729</q> </rational>
    </row>
    <row>
      <rational> <p>  9017</p> <q> 3168</q> </rational>
      <rational> <p>  -355</p> <q>   33</q> </rational>
      <rational> <p> 46732</p> <q> 5247</q> </rational>
      <rational> <p>    49</p> <q>  176</q> </rational>
      <rational> <p> -5103</p> <q>18656</q> </rational>
    </row>
    <row>
      <rational> <p>    35</p> <q>  384</q> </rational>
      <zero/>
      <rational> <p>   500</p> <q> 1113</q> </rational>
      <rational> <p>   125</p> <q>  192</q> </rational>
      <rational> <p> -2187</p> <q> 6784</q> </rational>
      <rational> <p>    11</p> <q>   84</q> </rational>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p>    35</p> <q>  384</q> </rational>
    <zero/>
    <rational> <p>   500</p> <q> 1113</q> </rational>
    <rational> <p>   125</p> <q>  192</q> </rational>
    <rational> <p> -2187</p> <q> 6784</q> </rational>
    <rational> <p>    11</p> <q>   84</q> </rational>
    <zero/>
  </estimation-weights>

  <error-weights>
    <rational> <p>    71</p> <q> 57600</q> </rational>
    <zero/>
    <rational> <p>   -71</p> <q> 16695</q> </rational>
    <rational> <p>    71</p> <q>  1920</q> </rational>
    <rational> <p>-17253</p> <q>339200</q> </rational>
    <rational> <p>    22</p> <q>   525</q> </rational>
    <rational> <p>    -1</p> <q>    40</q> </rational>
  </error-weights>

</Runge-Kutta>
