<?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: Zonneveld.xml,v 1.1 2004/05/23 18:47:22 luc Exp $ -->

<Runge-Kutta name="Zonneveld" >

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

  <internal-weights>
    <row>
      <!-- empty first row -->
    </row>
    <row>
      <rational> <p> 1</p> <q>2</q> </rational>
    </row>
    <row>
      <zero/>
      <rational> <p> 1</p> <q>2</q> </rational>
    </row>
    <row>
      <zero/>
      <zero/>
      <one/>
    </row>
    <row>
      <rational> <p> 5</p> <q>32</q> </rational>
      <rational> <p> 7</p> <q>32</q> </rational>
      <rational> <p>13</p> <q>32</q> </rational>
      <rational> <p>-1</p> <q>32</q> </rational>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p>1</p> <q>6</q> </rational>
    <rational> <p>1</p> <q>3</q> </rational>
    <rational> <p>1</p> <q>3</q> </rational>
    <rational> <p>1</p> <q>6</q> </rational>
    <zero/>
  </estimation-weights>

  <error-weights>
    <rational> <p> -2</p> <q>3</q> </rational>
    <integer>2</integer>
    <integer>2</integer>
    <integer>2</integer>
    <rational> <p>-16</p> <q>3</q> </rational>
  </error-weights>

</Runge-Kutta>
