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

<Runge-Kutta name="Higham and Hall" >

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

  <internal-weights>
    <row>
      <!-- empty first row -->
    </row>
    <row>
      <rational> <p>  2</p> <q>  9</q> </rational>
    </row>
    <row>
      <rational> <p>  1</p> <q> 12</q> </rational>
      <rational> <p>  1</p> <q>  4</q> </rational>
    </row>
    <row>
      <rational> <p>  1</p> <q>  8</q> </rational>
      <zero/>
      <rational> <p>  3</p> <q>  8</q> </rational>
    </row>
    <row>
      <rational> <p> 91</p> <q>500</q> </rational>
      <rational> <p>-27</p> <q>100</q> </rational>
      <rational> <p> 78</p> <q>125</q> </rational>
      <rational> <p>  8</p> <q>125</q> </rational>
    </row>
    <row>
      <rational> <p>-11</p> <q> 20</q> </rational>
      <rational> <p> 27</p> <q> 20</q> </rational>
      <rational> <p> 12</p> <q>  5</q> </rational>
      <rational> <p>-36</p> <q>  5</q> </rational>
      <integer>5</integer>
    </row>
    <row>
      <rational> <p>  1</p> <q> 12</q> </rational>
      <zero/>
      <rational> <p> 27</p> <q> 32</q> </rational>
      <rational> <p> -4</p> <q>  3</q> </rational>
      <rational> <p>125</p> <q> 96</q> </rational>
      <rational> <p>  5</p> <q> 48</q> </rational>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p>  1</p> <q> 12</q> </rational>
    <zero/>
    <rational> <p> 27</p> <q> 32</q> </rational>
    <rational> <p> -4</p> <q>  3</q> </rational>
    <rational> <p>125</p> <q> 96</q> </rational>
    <rational> <p>  5</p> <q> 48</q> </rational>
    <zero/>
  </estimation-weights>

  <error-weights>
    <rational> <p> -1</p> <q> 20</q> </rational>
    <zero/>
    <rational> <p> 81</p> <q>160</q> </rational>
    <rational> <p> -6</p> <q>  5</q> </rational>
    <rational> <p> 25</p> <q> 32</q> </rational>
    <rational> <p>  1</p> <q> 16</q> </rational>
    <rational> <p> -1</p> <q> 10</q> </rational>
  </error-weights>

</Runge-Kutta>
