<?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: Verner.xml,v 1.1 2004/05/23 19:38:10 luc Exp $ -->

<Runge-Kutta name="Verner" >

  <time-steps>
    <zero/>
    <rational> <p>1</p> <q> 6</q> </rational>
    <rational> <p>4</p> <q>15</q> </rational>
    <rational> <p>2</p> <q> 3</q> </rational>
    <rational> <p>5</p> <q> 6</q> </rational>
    <one/>
    <rational> <p>1</p> <q>15</q> </rational>
    <one/>
  </time-steps>

  <internal-weights>
    <row>
      <!-- empty first row -->
    </row>
    <row>
      <rational> <p>     1</p> <q>    6</q> </rational>
    </row>
    <row>
      <rational> <p>     4</p> <q>   75</q> </rational>
      <rational> <p>    16</p> <q>   75</q> </rational>
    </row>
    <row>
      <rational> <p>     5</p> <q>    6</q> </rational>
      <rational> <p>    -8</p> <q>    3</q> </rational>
      <rational> <p>     5</p> <q>    2</q> </rational>
    </row>
    <row>
      <rational> <p>  -165</p> <q>   64</q> </rational>
      <rational> <p>    55</p> <q>    6</q> </rational>
      <rational> <p>  -425</p> <q>   64</q> </rational>
      <rational> <p>    85</p> <q>   96</q> </rational>
    </row>
    <row>
      <rational> <p>    12</p> <q>    5</q> </rational>
      <integer>-8</integer>
      <rational> <p>  4015</p> <q>  612</q> </rational>
      <rational> <p>   -11</p> <q>   36</q> </rational>
      <rational> <p>    88</p> <q>  255</q> </rational>
    </row>
    <row>
      <rational> <p> -8263</p> <q>15000</q> </rational>
      <rational> <p>   124</p> <q>   75</q> </rational>
      <rational> <p>  -643</p> <q>  680</q> </rational>
      <rational> <p>   -81</p> <q>  250</q> </rational>
      <rational> <p>  2484</p> <q>10625</q> </rational>
      <zero/>
    </row>
    <row>
      <rational> <p>  3501</p> <q> 1720</q> </rational>
      <rational> <p>  -300</p> <q>   43</q> </rational>
      <rational> <p>297275</p> <q>52632</q> </rational>
      <rational> <p>  -319</p> <q> 2322</q> </rational>
      <rational> <p> 24068</p> <q>84065</q> </rational>
      <zero/>
      <rational> <p>  3850</p> <q>26703</q> </rational>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p>   3</p> <q>   40</q> </rational>
    <zero/>
    <rational> <p> 875</p> <q> 2244</q> </rational>
    <rational> <p>  23</p> <q>   72</q> </rational>
    <rational> <p> 264</p> <q> 1955</q> </rational>
    <zero/>
    <rational> <p> 125</p> <q>11592</q> </rational>
    <rational> <p>  43</p> <q>  616</q> </rational>
  </estimation-weights>

  <error-weights>
    <rational> <p>   1</p> <q>  160</q> </rational>
    <zero/>
    <rational> <p> 125</p> <q>17952</q> </rational>
    <rational> <p>  -1</p> <q>  144</q> </rational>
    <rational> <p>  12</p> <q> 1955</q> </rational>
    <rational> <p>   3</p> <q>   44</q> </rational>
    <rational> <p>-125</p> <q>11592</q> </rational>
    <rational> <p> -43</p> <q>  616</q> </rational>
  </error-weights>

</Runge-Kutta>
