duffing.xmds

XMDS is a code generator that integrates equations. You write them down in human readable form in a

<?xml version="1.0"?>
<simulation>
  
<!-- $Id: duffing.xmds,v 1.1 2004/06/22 10:18:58 paultcochrane Exp $ -->

<!--  Copyright (C) 2000-2004                                           -->
<!--                                                                    -->
<!--  Code contributed by Greg Collecutt, Joseph Hope and Paul Cochrane -->
<!--                                                                    -->
<!--  This file is part of xmds.                                        -->
<!--                                                                    -->
<!--  This program is free software; you can redistribute it and/or     -->
<!--  modify it under the terms of the GNU General Public License       -->
<!--  as published by the Free Software Foundation; either version 2    -->
<!--  of the License, or (at your option) any later version.            -->
<!--                                                                    -->
<!--  This program is distributed in the hope that it will be useful,   -->
<!--  but WITHOUT ANY WARRANTY; without even the implied warranty of    -->
<!--  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the     -->
<!--  GNU General Public License for more details.                      -->
<!--                                                                    -->
<!--  You should have received a copy of the GNU General Public License -->
<!--  along with this program; if not, write to the Free Software       -->
<!--  Foundation, Inc., 59 Temple Place - Suite 330, Boston,            -->
<!--  MA  02111-1307, USA.                                              -->

  <name> duffing </name>      <!-- the name of the simulation -->
  
  <author> Paul Cochrane </author>  <!-- the author of the simulation -->
  <description>
    <!-- a description of what the simulation is supposed to do -->
    Example simulation of Duffing's equation which describes the
    motion of a mechanical system in a twin-well potential.
  </description>
  
  <!-- Global system parameters and functionality -->
  <prop_dim> t </prop_dim>    <!-- name of main propagation dim -->
  
  <error_check> yes </error_check>   <!-- defaults to yes -->
  <use_wisdom> yes </use_wisdom>     <!-- defaults to no -->
  <benchmark> yes </benchmark>       <!-- defaults to no -->
  <use_prefs> yes </use_prefs>       <!-- defaults to yes -->
  
  <!-- Global variables for the simulation -->
  <globals>
  <![CDATA[
    const double xo = 1;      // initial x
    const double yo = 2;      // initial y
    const double k = 0.01;    // damping coefficient
  ]]>
  </globals>
  
  <!-- Field to be integrated over -->
  <field>
    <name> main </name>
    <samples> 1 </samples>       <!-- sample 1st point of dim? -->
    
    <vector>
      <name> main </name>
      <type> double </type>           <!-- data type of vector -->
      <components> x y </components>       <!-- names of components -->
      <![CDATA[
        x = xo;
	y = yo;
      ]]>
    </vector>
  </field>
  
  <!-- The sequence of integrations to perform -->
  <sequence>
    <integrate>
      <algorithm> RK4EX </algorithm> <!-- RK4EX, RK4IP, SIEX, SIIP -->
      <interval> 1000 </interval>
      <lattice> 100000 </lattice>     <!-- no. points in main dim -->
      <samples> 10000 </samples> <!-- no. pts in output moment group -->
      <![CDATA[
        dx_dt = y;
	dy_dt = -k*y + x*(1-x*x);
      ]]>
    </integrate>
  </sequence>
  
  <!-- The output to generate -->
  <output format="ascii">
    <group>
      <sampling>
        <moments> yOut xOut </moments>   <!-- names of moments -->
        <![CDATA[
          xOut = x;
	  yOut = y;
        ]]>
      </sampling>
    </group>
  </output>
  
</simulation>