<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>van_der_pol</name>
  <author>Graham Dennis</author>
  <description>
    Van der Pol oscillator. An example of a stiff equation.
  </description>
  
  <features>
    <benchmark />
    <error_check />
    <bing />
    <!-- That's right, this script breaks the shackles with FFTW! -->
    <arguments>
      <argument name="lambda" type="real" default_value="100.0" />
      <![CDATA[
        _LOG(_SIMULATION_LOG_LEVEL, "lambda is %e\n", lambda);
      ]]>
    </arguments>
  </features>
  
  <geometry>
    <propagation_dimension> t </propagation_dimension>
  </geometry>
  
  <vector name="main" type="real">
    <components>
      y yDot
    </components>
    <initialisation>
      <![CDATA[
      y = 1.0;
      yDot = 0.0;
      ]]>
    </initialisation>
  </vector>
  
  <sequence>
    <integrate algorithm="ARK89" interval="100.0" steps="25000" tolerance="1e-7">
      <samples>5000</samples>
      <operators>
        <integration_vectors>main</integration_vectors>
        <![CDATA[
        dy_dt = yDot;
        dyDot_dt = lambda*(1.0 - y*y)*yDot - y;
        
        ]]>
      </operators>
    </integrate>
  </sequence>
  <output>
      <sampling_group initial_sample="yes">
        <moments>yR yDotR</moments>
        <dependencies>main</dependencies>
        <![CDATA[
          yR = y;
          yDotR = yDot;
        ]]>
      </sampling_group>
  </output>
</simulation>