Examples of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

Package org.apache.commons.math.ode.nonstiff

Examples of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator
This class implements the 5(4) Dormand-Prince integrator for Ordinary Differential Equations.
This integrator is an embedded Runge-Kutta integrator of order 5(4) used in local extrapolation mode (i.e. the solution is computed using the high order formula) with stepsize control (and automatic step initialization) and continuous output. This method uses 7 functions evaluations per step. However, since this is an fsal, the last evaluation of one step is the same as the first evaluation of the next step and hence can be avoided. So the cost is really 6 functions evaluations per step.

This method has been published (whithout the continuous output that was added by Shampine in 1986) in the following article :
```
 A family of embedded Runge-Kutta formulae J. R. Dormand and P. J. Prince Journal of Computational and Applied Mathematics volume 6, no 1, 1980, pp. 19-26 
```
@version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ @since 1.2


    @Test
    public void testHighAccuracyExternalDifferentiation()
        throws IntegratorException, DerivativeException {
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, 1.0e-10, 1.0e-10);
        double hP = 1.0e-12;
        SummaryStatistics residualsP0 = new SummaryStatistics();
        SummaryStatistics residualsP1 = new SummaryStatistics();
        for (double b = 2.88; b < 3.08; b += 0.001) {
            Brusselator brusselator = new Brusselator(b);
            double[] y = { 1.3, b };
            integ.integrate(brusselator, 0, y, 20.0, y);
            double[] yP = { 1.3, b + hP };
            brusselator.setParameter(0, b + hP);
            integ.integrate(brusselator, 0, yP, 20.0, yP);
            residualsP0.addValue((yP[0] - y[0]) / hP - brusselator.dYdP0());
            residualsP1.addValue((yP[1] - y[1]) / hP - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) > 0.02);
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) < 0.03);

View Full Code Here


    @Test
    public void testInternalDifferentiation()
        throws IntegratorException, DerivativeException {
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, 1.0e-4, 1.0e-4);
        double hP = 1.0e-12;
        SummaryStatistics residualsP0 = new SummaryStatistics();
        SummaryStatistics residualsP1 = new SummaryStatistics();
        for (double b = 2.88; b < 3.08; b += 0.001) {
            Brusselator brusselator = new Brusselator(b);
            brusselator.setParameter(0, b);
            double[] z = { 1.3, b };
            double[][] dZdZ0 = new double[2][2];
            double[][] dZdP  = new double[2][1];
            double hY = 1.0e-12;
            FirstOrderIntegratorWithJacobians extInt =
                new FirstOrderIntegratorWithJacobians(integ, brusselator, new double[] { b },
                                                      new double[] { hY, hY }, new double[] { hP });
            extInt.setMaxEvaluations(5000);
            extInt.integrate(0, z, new double[][] { { 0.0 }, { 1.0 } }, 20.0, z, dZdZ0, dZdP);
            Assert.assertEquals(5000, extInt.getMaxEvaluations());
            Assert.assertTrue(extInt.getEvaluations() > 2000);
            Assert.assertTrue(extInt.getEvaluations() < 2500);
            Assert.assertEquals(4 * integ.getEvaluations(), extInt.getEvaluations());
            residualsP0.addValue(dZdP[0][0] - brusselator.dYdP0());
            residualsP1.addValue(dZdP[1][0] - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) < 0.006);
        Assert.assertTrue(residualsP0.getStandardDeviation() < 0.0009);

View Full Code Here


    @Test
    public void testAnalyticalDifferentiation()
        throws IntegratorException, DerivativeException {
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, 1.0e-4, 1.0e-4);
        SummaryStatistics residualsP0 = new SummaryStatistics();
        SummaryStatistics residualsP1 = new SummaryStatistics();
        for (double b = 2.88; b < 3.08; b += 0.001) {
            Brusselator brusselator = new Brusselator(b);
            brusselator.setParameter(0, b);
            double[] z = { 1.3, b };
            double[][] dZdZ0 = new double[2][2];
            double[][] dZdP  = new double[2][1];
            FirstOrderIntegratorWithJacobians extInt =
                new FirstOrderIntegratorWithJacobians(integ, brusselator);
            extInt.setMaxEvaluations(5000);
            extInt.integrate(0, z, new double[][] { { 0.0 }, { 1.0 } }, 20.0, z, dZdZ0, dZdP);
            Assert.assertEquals(5000, extInt.getMaxEvaluations());
            Assert.assertTrue(extInt.getEvaluations() > 510);
            Assert.assertTrue(extInt.getEvaluations() < 610);
            Assert.assertEquals(integ.getEvaluations(), extInt.getEvaluations());
            residualsP0.addValue(dZdP[0][0] - brusselator.dYdP0());
            residualsP1.addValue(dZdP[1][0] - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) < 0.004);
        Assert.assertTrue(residualsP0.getStandardDeviation() < 0.0008);

View Full Code Here

    }


    @Test
    public void testFinalResult() throws IntegratorException, DerivativeException {
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, 1.0e-10, 1.0e-10);
        double[] y = new double[] { 0.0, 1.0 };
        Circle circle = new Circle(y, 1.0, 1.0, 0.1);
        double[][] dydy0 = new double[2][2];
        double[][] dydp  = new double[2][3];
        double t = 18 * Math.PI;

View Full Code Here

    }


    @Test
    public void testStepHandlerResult() throws IntegratorException, DerivativeException {
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, 1.0e-10, 1.0e-10);
        double[] y = new double[] { 0.0, 1.0 };
        final Circle circle = new Circle(y, 1.0, 1.0, 0.1);
        double[][] dydy0 = new double[2][2];
        double[][] dydp  = new double[2][3];
        double t = 18 * Math.PI;

View Full Code Here

    }


    @Test
    public void testEventHandler() throws IntegratorException, DerivativeException {
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, 1.0e-10, 1.0e-10);
        double[] y = new double[] { 0.0, 1.0 };
        final Circle circle = new Circle(y, 1.0, 1.0, 0.1);
        double[][] dydy0 = new double[2][2];
        double[][] dydp  = new double[2][3];
        double t = 18 * Math.PI;

View Full Code Here

  @Override
  public void setUp() {
    pb = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    integ = new DormandPrince54Integrator(minStep, maxStep, 1.0e-8, 1.0e-8);
  }

View Full Code Here

  @Override
  public void setUp() {
    pb = new TestProblem3(0.9);
    double minStep = 0;
    double maxStep = pb.getFinalTime() - pb.getInitialTime();
    integ = new DormandPrince54Integrator(minStep, maxStep, 1.0e-8, 1.0e-8);
  }

View Full Code Here

        // essentially noise.
        // This test is taken from Hairer, Norsett and Wanner book
        // Solving Ordinary Differential Equations I (Nonstiff problems),
        // the curves dy/dp = g(b) are in figure 6.5
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, new double[] { 1.0e-4, 1.0e-4 }, new double[] { 1.0e-4, 1.0e-4 });
        double hP = 1.0e-12;
        SummaryStatistics residualsP0 = new SummaryStatistics();
        SummaryStatistics residualsP1 = new SummaryStatistics();
        for (double b = 2.88; b < 3.08; b += 0.001) {
            Brusselator brusselator = new Brusselator(b);
            double[] y = { 1.3, b };
            integ.integrate(brusselator, 0, y, 20.0, y);
            double[] yP = { 1.3, b + hP };
            brusselator.setParameter(0, b + hP);
            integ.integrate(brusselator, 0, yP, 20.0, yP);
            residualsP0.addValue((yP[0] - y[0]) / hP - brusselator.dYdP0());
            residualsP1.addValue((yP[1] - y[1]) / hP - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) > 600);
        Assert.assertTrue(residualsP0.getStandardDeviation() > 30);

View Full Code Here


    @Test
    public void testHighAccuracyExternalDifferentiation()
        throws IntegratorException, DerivativeException {
        FirstOrderIntegrator integ =
            new DormandPrince54Integrator(1.0e-8, 100.0, new double[] { 1.0e-10, 1.0e-10 }, new double[] { 1.0e-10, 1.0e-10 });
        double hP = 1.0e-12;
        SummaryStatistics residualsP0 = new SummaryStatistics();
        SummaryStatistics residualsP1 = new SummaryStatistics();
        for (double b = 2.88; b < 3.08; b += 0.001) {
            Brusselator brusselator = new Brusselator(b);
            double[] y = { 1.3, b };
            integ.integrate(brusselator, 0, y, 20.0, y);
            double[] yP = { 1.3, b + hP };
            brusselator.setParameter(0, b + hP);
            integ.integrate(brusselator, 0, yP, 20.0, yP);
            residualsP0.addValue((yP[0] - y[0]) / hP - brusselator.dYdP0());
            residualsP1.addValue((yP[1] - y[1]) / hP - brusselator.dYdP1());
        }
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) > 0.02);
        Assert.assertTrue((residualsP0.getMax() - residualsP0.getMin()) < 0.03);

View Full Code Here

0 1 2 3 4

TOP

Related Classes of org.apache.commons.math.ode.nonstiff.DormandPrince54Integrator

org.apache.commons.math.ode.ContinuousOutputModelTest

org.apache.commons.math.ode.jacobians.FirstOrderIntegratorWithJacobiansTest

org.apache.commons.math.ode.nonstiff.DormandPrince54IntegratorTest

org.apache.commons.math.ode.sampling.StepNormalizerTest

All source code are property of their respective owners. Java is a trademark of Sun Microsystems, Inc and owned by ORACLE Inc. Contact coftware#gmail.com.