<simulation>
  <header>
    <title lang="english">System of differential equations</title>
    <title>Système d'équations différentielles</title>
    <title lang="spanish">Sistema de ecuaciones diferenciales</title>
    <author>Stéphane Mottelet, Guillaume Barbaud</author>
    <keywords>simulation,scilab,xml</keywords>
    <keywords lang="spanish">Simulación, XML, Scilab</keywords>
  </header>
  <notes>
    <p>Une simulation très simple montrant la solution d'un système de deux équation différentielle linéaire
à coefficients constants.
    </p>
  </notes>
  <notes lang="english">
    <p>A very simple example showing the solution of  system of two linear ordinary differential 
    equation with constant coefficients.
    </p>
  </notes>
  <notes lang="german">
    <p />
  </notes>
  <notes lang="spanish">
    <p>Una simulación muy sencilla que muestra la solución de un sistema de dos ecuaciones diferenciales lineales con coeficientes constantes..</p>
  </notes>
  <parameters>
    <section>
      <title lang="english">Parameters of the equation</title>
      <title>Paramètres de l'équation</title>
      <title lang="spanish">Parametros de la ecuación</title>
      <database label="matriceA" editable="yes">
        <matrix label="a" cols="2" rows="2">
          <name>Matrice du système</name>
          <name lang="english">Matrix of the system</name>
          <name lang="spanish">Matriz del sistema</name>
          <row>
            <value>1 1</value>
          </row>
          <row>
            <value>0 1</value>
          </row>
        </matrix>
        <record>
          <name lang="english">Stable system</name>
          <name lang="french">Système stable</name>
          <name lang="spanish">Sistema estable</name>
          <matrix-value ref="a">
            <row>
              <value>-1 1</value>
            </row>
            <row>
              <value>0 -1</value>
            </row>
          </matrix-value>
        </record>
        <record>
          <name lang="french">Oscillateur</name>
          <name lang="english">Oscillator</name>
          <name lang="spanish">Oscilador</name>
          <matrix-value ref="a">
            <row>
              <value>0 1</value>
            </row>
            <row>
              <value>-1 0</value>
            </row>
          </matrix-value>
        </record>
        <record>
          <name lang="french">Système instable</name>
          <name lang="english">Unstable system</name>
          <name lang="spanish">Sistema inestable</name>
          <matrix-value ref="a">
            <row>
              <value>1 1</value>
            </row>
            <row>
              <value>0 1</value>
            </row>
          </matrix-value>
        </record>
        <record>
          <name lang="french">prout</name>
          <matrix-value ref="a">
            <row>
              <value>0 0</value>
            </row>
            <row>
              <value>0 -1</value>
            </row>
          </matrix-value>
        </record>
      </database>
      <subsection>
        <matrix label="xzero" cols="1" rows="2">
          <name>Condition initiale</name>
          <name>Initial condition</name>
          <name lang="english">x0</name>
          <name lang="spanish">Condiciones iníciales</name>
          <col>
            <value>1 1</value>
          </col>
        </matrix>
        <scalar label="tmax" min="1" max="20" increment="1">
          <name>Temps final</name>
          <name lang="english">Final time</name>
          <name lang="spanish">Tiempo final</name>
          <value>10</value>
        </scalar>
      </subsection>
    </section>
  </parameters>
  <compute>
    <defdomain1d label="t">
      <name lang="english">Time</name>
      <name>Temps</name>
      <name lang="spanish">Tiempo</name>
      <interval steps="256">
        <initialvalue>0</initialvalue>
        <finalvalue>tmax</finalvalue>
      </interval>
    </defdomain1d>
    <ode label="ode1">
      <refdomain1d ref="t" />
      <states>
        <state label="x" size="2">
          <name>x</name>
          <name lang="english">x</name>
          <name lang="spanish">X</name>
          <derivative>a*x</derivative>
          <initialcondition>xzero</initialcondition>
        </state>
      </states>
      <outputs>
        <output label="x1">
          <name>x1(t)</name>
          <name lang="english">x1(t)</name>
          <name lang="spanish">x1(t)</name>
          <value>x(:,1)</value>
        </output>
        <output label="x2">
          <name>x2(t)</name>
          <name lang="english">x2(t)</name>
          <name lang="spanish">x2(t)</name>
          <value>x(:,2)</value>
        </output>
      </outputs>
    </ode>
  </compute>
  <graphs />
  <display>
    <window>
      <axis2d xmin="0" xmax="tmax" ymin="min(x)" ymax="max(x)">
        <drawcurve2d ref="x1" />
        <drawcurve2d ref="x2" />
      </axis2d>
    </window>
  </display>
</simulation>