<?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: Fehlberg45.xml,v 1.1 2004/05/23 19:03:25 luc Exp $ -->

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

  <time-steps>
    <zero/>
    <rational> <p> 1</p> <q> 4</q> </rational>
    <rational> <p> 3</p> <q> 8</q> </rational>
    <rational> <p>12</p> <q>13</q> </rational>
    <one/>
    <rational> <p> 1</p> <q> 2</q> </rational>
  </time-steps>

  <internal-weights>
    <row>
      <!-- empty first row -->
    </row>
    <row>
      <rational> <p>    1</p> <q>   4</q> </rational>
    </row>
    <row>
      <rational> <p>    3</p> <q>  32</q> </rational>
      <rational> <p>    9</p> <q>  32</q> </rational>
    </row>
    <row>
      <rational> <p> 1932</p> <q>2197</q> </rational>
      <rational> <p>-7200</p> <q>2197</q> </rational>
      <rational> <p> 7296</p> <q>2197</q> </rational>
    </row>
    <row>
      <rational> <p>  439</p> <q> 216</q> </rational>
      <integer>-8</integer>
      <rational> <p> 3680</p> <q> 513</q> </rational>
      <rational> <p> -845</p> <q>4104</q> </rational>
    </row>
    <row>
      <rational> <p>   -8</p> <q>  27</q> </rational>
      <integer>2</integer>
      <rational> <p>-3544</p> <q>2565</q> </rational>
      <rational> <p> 1859</p> <q>4104</q> </rational>
      <rational> <p>  -11</p> <q>  40</q> </rational>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p>  25</p> <q> 216</q> </rational>
    <zero/>
    <rational> <p>1408</p> <q>2565</q> </rational>
    <rational> <p>2197</p> <q>4104</q> </rational>
    <rational> <p>  -1</p> <q>   5</q> </rational>
    <zero/>
  </estimation-weights>

  <error-weights>
    <rational> <p>    1</p> <q>  360</q> </rational>
    <zero/>
    <rational> <p> -128</p> <q> 4275</q> </rational>
    <rational> <p>-2197</p> <q>75240</q> </rational>
    <rational> <p>    1</p> <q>   50</q> </rational>
    <rational> <p>    2</p> <q>   55</q> </rational>
  </error-weights>

</Runge-Kutta>
