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

<!-- this is the 3/8 rule method -->
<Runge-Kutta name="3/8 rule" >

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

  <internal-weights>
    <row>
      <!-- empty first row -->
    </row>
    <row>
      <rational> <p>1</p> <q>3</q> </rational>
    </row>
    <row>
      <rational> <p>-1</p> <q>3</q> </rational> <one/>
    </row>
    <row>
      <one/> <integer>-1</integer> <one/>
    </row>
  </internal-weights>

  <estimation-weights>
    <rational> <p>1</p> <q>8</q> </rational>
    <rational> <p>3</p> <q>8</q> </rational>
    <rational> <p>3</p> <q>8</q> </rational>
    <rational> <p>1</p> <q>8</q> </rational>
  </estimation-weights>

</Runge-Kutta>
