Examples of org.apache.commons.math.ode.EulerIntegrator

org.apache.commons.math.ode.EulerIntegrator
This class implements a simple Euler integrator for Ordinary Differential Equations.
The Euler algorithm is the simplest one that can be used to integrate ordinary differential equations. It is a simple inversion of the forward difference expression : f'=(f(t+h)-f(t))/h which leads to f(t+h)=f(t)+hf'. The interpolation scheme used for dense output is the linear scheme already used for integration.

This algorithm looks cheap because it needs only one function evaluation per step. However, as it uses linear estimates, it needs very small steps to achieve high accuracy, and small steps lead to numerical errors and instabilities.

This algorithm is almost never used and has been included in this package only as a comparison reference for more useful integrators.
@see MidpointIntegrator @see ClassicalRungeKuttaIntegrator @see GillIntegrator @see ThreeEighthesIntegrator @version $Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $ @since 1.2

  }


  public void testDimensionCheck() {
    try  {
      TestProblem1 pb = new TestProblem1();
      new EulerIntegrator(0.01).integrate(pb,
                                          0.0, new double[pb.getDimension()+10],
                                          1.0, new double[pb.getDimension()+10]);
        fail("an exception should have been thrown");
    } catch(DerivativeException de) {
      fail("wrong exception caught");

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        TestProblemAbstract pb  = (TestProblemAbstract) problems[k].clone();
        double step = (pb.getFinalTime() - pb.getInitialTime())
          * Math.pow(2.0, -i);


        FirstOrderIntegrator integ = new EulerIntegrator(step);
        TestProblemHandler handler = new TestProblemHandler(pb, integ);
        integ.setStepHandler(handler);
        SwitchingFunction[] functions = pb.getSwitchingFunctions();
        for (int l = 0; l < functions.length; ++l) {
          integ.addSwitchingFunction(functions[l],
                                     Double.POSITIVE_INFINITY, 1.0e-6 * step, 1000);
        }
        integ.integrate(pb,
                        pb.getInitialTime(), pb.getInitialState(),
                        pb.getFinalTime(), new double[pb.getDimension()]);


        double error = handler.getMaximalValueError();
        if (i > 4) {

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    throws DerivativeException, IntegratorException {


    TestProblem1 pb  = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;


    FirstOrderIntegrator integ = new EulerIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.setStepHandler(handler);
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


   assertTrue(handler.getLastError() < 2.0e-4);
   assertTrue(handler.getMaximalValueError() < 1.0e-3);
   assertEquals(0, handler.getMaximalTimeError(), 1.0e-12);
   assertEquals("Euler", integ.getName());


  }

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    throws DerivativeException, IntegratorException {


    TestProblem1 pb  = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.2;


    FirstOrderIntegrator integ = new EulerIntegrator(step);
    TestProblemHandler handler = new TestProblemHandler(pb, integ);
    integ.setStepHandler(handler);
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    assertTrue(handler.getLastError() > 0.01);
    assertTrue(handler.getMaximalValueError() > 0.2);

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    throws DerivativeException, IntegratorException,
           IOException, ClassNotFoundException {


    TestProblem1 pb = new TestProblem1();
    double step = (pb.getFinalTime() - pb.getInitialTime()) * 0.001;
    EulerIntegrator integ = new EulerIntegrator(step);
    integ.setStepHandler(new ContinuousOutputModel());
    integ.integrate(pb,
                    pb.getInitialTime(), pb.getInitialState(),
                    pb.getFinalTime(), new double[pb.getDimension()]);


    ByteArrayOutputStream bos = new ByteArrayOutputStream();
    ObjectOutputStream    oos = new ObjectOutputStream(bos);
    oos.writeObject(integ.getStepHandler());


    assertTrue(bos.size () > 82000);
    assertTrue(bos.size () < 83000);


    ByteArrayInputStream  bis = new ByteArrayInputStream(bos.toByteArray());

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Related Classes of org.apache.commons.math.ode.EulerIntegrator

org.apache.commons.math.ode.EulerIntegratorTest

org.apache.commons.math.ode.EulerStepInterpolatorTest

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