<?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: Gill.xml,v 1.2 2004/05/23 17:41:52 luc Exp $ -->

<Runge-Kutta name="Gill" >

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

  <internal-weights>
    <row>
      <!-- empty first row -->
    </row>
    <row>
      <rational> <p>1</p> <q>2</q> </rational>
    </row>
    <row>
      <quadratic-surd> <p1>-1</p1> <p2> 1</p2> <d>2</d> <q>2</q> </quadratic-surd>
      <quadratic-surd> <p1> 2</p1> <p2>-1</p2> <d>2</d> <q>2</q> </quadratic-surd>
    </row>
    <row>
      <zero/>
      <quadratic-surd> <p1> 0</p1> <p2>-1</p2> <d>2</d> <q>2</q> </quadratic-surd>
      <quadratic-surd> <p1> 2</p1> <p2> 1</p2> <d>2</d> <q>2</q> </quadratic-surd>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p>1</p> <q>6</q> </rational>
    <quadratic-surd> <p1> 2</p1> <p2>-1</p2> <d>2</d> <q>6</q> </quadratic-surd>
    <quadratic-surd> <p1> 2</p1> <p2> 1</p2> <d>2</d> <q>6</q> </quadratic-surd>
    <rational> <p>1</p> <q>6</q> </rational>
  </estimation-weights>

</Runge-Kutta>
