<?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: Fehlberg78.xml,v 1.1 2004/05/23 19:22:52 luc Exp $ -->

<Runge-Kutta name="Fehlberg 7(8)" >

  <time-steps>
    <zero/>
    <rational> <p>2</p> <q>27</q> </rational>
    <rational> <p>1</p> <q> 9</q> </rational>
    <rational> <p>1</p> <q> 6</q> </rational>
    <rational> <p>5</p> <q>12</q> </rational>
    <rational> <p>1</p> <q> 2</q> </rational>
    <rational> <p>5</p> <q> 6</q> </rational>
    <rational> <p>1</p> <q> 6</q> </rational>
    <rational> <p>2</p> <q> 3</q> </rational>
    <rational> <p>1</p> <q> 3</q> </rational>
    <one/>
    <zero/>
    <one/>
  </time-steps>

  <internal-weights>
    <row>
      <!-- empty first row -->
    </row>
    <row>
      <rational> <p>    2</p> <q>  27</q> </rational>
    </row>
    <row>
      <rational> <p>    1</p> <q>  36</q> </rational>
      <rational> <p>    1</p> <q>  12</q> </rational>
    </row>
    <row>
      <rational> <p>    1</p> <q>  24</q> </rational>
      <zero/>
      <rational> <p>    1</p> <q>   8</q> </rational>
    </row>
    <row>
      <rational> <p>    5</p> <q>  12</q> </rational>
      <zero/>
      <rational> <p>  -25</p> <q>  16</q> </rational>
      <rational> <p>   25</p> <q>  16</q> </rational>
    </row>
    <row>
      <rational> <p>    1</p> <q>  20</q> </rational>
      <zero/>
      <zero/>
      <rational> <p>    1</p> <q>   4</q> </rational>
      <rational> <p>    1</p> <q>   5</q> </rational>
    </row>
    <row>
      <rational> <p>  -25</p> <q> 108</q> </rational>
      <zero/>
      <zero/>
      <rational> <p>  125</p> <q> 108</q> </rational>
      <rational> <p>  -65</p> <q>  27</q> </rational>
      <rational> <p>  125</p> <q>  54</q> </rational>
    </row>
    <row>
      <rational> <p>   31</p> <q> 300</q> </rational>
      <zero/>
      <zero/>
      <zero/>
      <rational> <p>   61</p> <q> 225</q> </rational>
      <rational> <p>   -2</p> <q>   9</q> </rational>
      <rational> <p>   13</p> <q> 900</q> </rational>
    </row>
    <row>
      <integer>2</integer>
      <zero/>
      <zero/>
      <rational> <p>  -53</p> <q>   6</q> </rational>
      <rational> <p>  704</p> <q>  45</q> </rational>
      <rational> <p> -107</p> <q>   9</q> </rational>
      <rational> <p>   67</p> <q>  90</q> </rational>
      <integer>3</integer>
    </row>
    <row>
      <rational> <p>  -91</p> <q> 108</q> </rational>
      <zero/>
      <zero/>
      <rational> <p>   23</p> <q> 108</q> </rational>
      <rational> <p> -976</p> <q> 135</q> </rational>
      <rational> <p>  311</p> <q>  54</q> </rational>
      <rational> <p>  -19</p> <q>  60</q> </rational>
      <rational> <p>   17</p> <q>   6</q> </rational>
      <rational> <p>   -1</p> <q>   12</q> </rational>
    </row>
    <row>
      <rational> <p> 2383</p> <q>4100</q> </rational>
      <zero/>
      <zero/>
      <rational> <p> -341</p> <q> 164</q> </rational>
      <rational> <p> 4496</p> <q>1025</q> </rational>
      <rational> <p> -301</p> <q>  82</q> </rational>
      <rational> <p> 2133</p> <q>4100</q> </rational>
      <rational> <p>   45</p> <q>  82</q> </rational>
      <rational> <p>   45</p> <q> 164</q> </rational>
      <rational> <p>   18</p> <q>  41</q> </rational>
    </row>
    <row>
      <rational> <p>    3</p> <q> 205</q> </rational>
      <zero/>
      <zero/>
      <zero/>
      <zero/>
      <rational> <p>   -6</p> <q>  41</q> </rational>
      <rational> <p>   -3</p> <q> 205</q> </rational>
      <rational> <p>   -3</p> <q>  41</q> </rational>
      <rational> <p>    3</p> <q>  41</q> </rational>
      <rational> <p>    6</p> <q>  41</q> </rational>
      <zero/>
    </row>
    <row>
      <rational> <p>-1777</p> <q>4100</q> </rational>
      <zero/>
      <zero/>
      <rational> <p> -341</p> <q> 164</q> </rational>
      <rational> <p> 4496</p> <q>1025</q> </rational>
      <rational> <p> -289</p> <q>  82</q> </rational>
      <rational> <p> 2193</p> <q>4100</q> </rational>
      <rational> <p>   51</p> <q>  82</q> </rational>
      <rational> <p>   33</p> <q> 164</q> </rational>
      <rational> <p>   12</p> <q>  41</q> </rational>
      <zero/>
      <one/>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p> 41</p> <q>840</q> </rational>
    <zero/>
    <zero/>
    <zero/>
    <zero/>
    <rational> <p> 34</p> <q>105</q> </rational>
    <rational> <p>  9</p> <q> 35</q> </rational>
    <rational> <p>  9</p> <q> 35</q> </rational>
    <rational> <p>  9</p> <q>280</q> </rational>
    <rational> <p>  9</p> <q>280</q> </rational>
    <rational> <p> 41</p> <q>840</q> </rational>
    <zero/>
    <zero/>
  </estimation-weights>

  <error-weights>
    <rational> <p>-41</p> <q>840</q> </rational>
    <zero/>
    <zero/>
    <zero/>
    <zero/>
    <zero/>
    <zero/>
    <zero/>
    <zero/>
    <zero/>
    <rational> <p>-41</p> <q>840</q> </rational>
    <rational> <p> 41</p> <q>840</q> </rational>
    <rational> <p> 41</p> <q>840</q> </rational>
  </error-weights>

</Runge-Kutta>
