<?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: CashKarp.xml,v 1.3 2004/05/23 17:41:52 luc Exp $ -->

<Runge-Kutta name="Cash-Karp" >

  <time-steps>
    <zero/>
    <rational> <p>1</p> <q> 5</q> </rational>
    <rational> <p>3</p> <q>10</q> </rational>
    <rational> <p>3</p> <q> 5</q> </rational>
    <one/>
    <rational> <p>7</p> <q> 8</q> </rational>
  </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>    3</p> <q>    10</q> </rational>
      <rational> <p>   -9</p> <q>    10</q> </rational>
      <rational> <p>    6</p> <q>     5</q> </rational>
    </row>
    <row>
      <rational> <p>  -11</p> <q>    54</q> </rational>
      <rational> <p>    5</p> <q>     2</q> </rational>
      <rational> <p>  -70</p> <q>    27</q> </rational>
      <rational> <p>   35</p> <q>    27</q> </rational>
    </row>
    <row>
      <rational> <p> 1631</p> <q> 55296</q> </rational>
      <rational> <p>  175</p> <q>   512</q> </rational>
      <rational> <p>  575</p> <q> 13824</q> </rational>
      <rational> <p>44275</p> <q>110592</q> </rational>
      <rational> <p>  253</p> <q>  4096</q> </rational>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p>   37</p> <q>   378</q> </rational>
    <zero/>
    <rational> <p>  250</p> <q>   621</q> </rational>
    <rational> <p>  125</p> <q>   594</q> </rational>
    <zero/>
    <rational> <p>  512</p> <q>  1771</q> </rational>
  </estimation-weights>

  <error-weights>
    <rational> <p> -277</p> <q> 64512</q> </rational>
    <zero/>
    <rational> <p> 6925</p> <q>370944</q> </rational>
    <rational> <p>-6925</p> <q>202752</q> </rational>
    <rational> <p> -277</p> <q> 14336</q> </rational>
    <rational> <p>  277</p> <q>  7084</q> </rational>
  </error-weights>

</Runge-Kutta>
