Examples of org.apache.commons.math3.ode.nonstiff.DormandPrince853Integrator

Package org.apache.commons.math3.ode.nonstiff

Examples of org.apache.commons.math3.ode.nonstiff.DormandPrince853Integrator

org.apache.commons.math3.ode.nonstiff.DormandPrince853Integrator
This class implements the 8(5,3) Dormand-Prince integrator for Ordinary Differential Equations.
This integrator is an embedded Runge-Kutta integrator of order 8(5,3) 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 12 functions evaluations per step for integration and 4 evaluations for interpolation. However, since the first interpolation evaluation is the same as the first integration evaluation of the next step, we have included it in the integrator rather than in the interpolator and specified the method was an fsal. Hence, despite we have 13 stages here, the cost is really 12 evaluations per step even if no interpolation is done, and the overcost of interpolation is only 3 evaluations.

This method is based on an 8(6) method by Dormand and Prince (i.e. order 8 for the integration and order 6 for error estimation) modified by Hairer and Wanner to use a 5th order error estimator with 3rd order correction. This modification was introduced because the original method failed in some cases (wrong steps can be accepted when step size is too large, for example in the Brusselator problem) and also had severe difficulties when applied to problems with discontinuities. This modification is explained in the second edition of the first volume (Nonstiff Problems) of the reference book by Hairer, Norsett and Wanner: Solving Ordinary Differential Equations (Springer-Verlag, ISBN 3-540-56670-8).
@since 1.2

            public void computeDerivatives(double t, double[] y, double[] yDot) {
                yDot[0] = 1.0;
            }
        };


        DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.001, 1000, 1.0e-14, 1.0e-14);
        integrator.addEventHandler(new ResettingEvent(10.99), 0.1, 1.0e-9, 1000);
        integrator.addEventHandler(new ResettingEvent(11.01), 0.1, 1.0e-9, 1000);
        integrator.setInitialStepSize(3.0);


        double target = 30.0;
        double[] y = new double[1];
        double tEnd = integrator.integrate(equation, 0.0, y, target, y);
        Assert.assertEquals(target, tEnd, 1.0e-10);
        Assert.assertEquals(32.0, y[0], 1.0e-10);


    }

View Full Code Here

                secondaryDot[0] = -3.0;
            }
        });
        int index = equation.getSecondaryMappers()[0].getFirstIndex();


        DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.001, 1000, 1.0e-14, 1.0e-14);
        integrator.addEventHandler(new SecondaryStateEvent(index, -3.0), 0.1, 1.0e-9, 1000);
        integrator.setInitialStepSize(3.0);


        integrator.integrate(equation, 30.0);
        Assert.assertEquals( 1.0, equation.getTime(), 1.0e-10);
        Assert.assertEquals( 2.0, equation.getPrimaryState()[0], 1.0e-10);
        Assert.assertEquals(-3.0, equation.getSecondaryState(0)[0], 1.0e-10);


    }

View Full Code Here

            throw new NumberIsTooSmallException(
                  LocalizedFormats.INTEGRATION_METHOD_NEEDS_AT_LEAST_TWO_PREVIOUS_POINTS,
                  nSteps, 2, true);
        }


        starter = new DormandPrince853Integrator(minStep, maxStep,
                                                 scalAbsoluteTolerance,
                                                 scalRelativeTolerance);
        this.nSteps = nSteps;


        exp = -1.0 / order;

View Full Code Here

                                  final int order,
                                  final double minStep, final double maxStep,
                                  final double[] vecAbsoluteTolerance,
                                  final double[] vecRelativeTolerance) {
        super(name, minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);
        starter = new DormandPrince853Integrator(minStep, maxStep,
                                                 vecAbsoluteTolerance,
                                                 vecRelativeTolerance);
        this.nSteps = nSteps;


        exp = -1.0 / order;

View Full Code Here

    public void testIncreasingOnly()
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = new DormandPrince853Integrator(1.0e-3, 100.0, 1e-7, 1e-7);
        Event allEvents = new Event(true, true);
        integrator.addEventHandler(allEvents, 0.1, e, 1000,
                                   new BracketingNthOrderBrentSolver(1.0e-7, 5));
        Event onlyIncreasing = new Event(false, true);
        integrator.addEventHandler(new EventFilter(onlyIncreasing,

View Full Code Here

    public void testDecreasingOnly()
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = new DormandPrince853Integrator(1.0e-3, 100.0, 1e-7, 1e-7);
        Event allEvents = new Event(true, true);
        integrator.addEventHandler(allEvents, 0.1, e, 1000,
                                   new BracketingNthOrderBrentSolver(1.0e-7, 5));
        Event onlyDecreasing = new Event(true, false);
        integrator.addEventHandler(new EventFilter(onlyDecreasing,

View Full Code Here

    public void testTwoOppositeFilters()
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = new DormandPrince853Integrator(1.0e-3, 100.0, 1e-7, 1e-7);
        Event allEvents = new Event(true, true);
        integrator.addEventHandler(allEvents, 0.1, e, 1000,
                                   new BracketingNthOrderBrentSolver(1.0e-7, 5));
        Event onlyIncreasing = new Event(false, true);
        integrator.addEventHandler(new EventFilter(onlyIncreasing,

View Full Code Here

     */
    public void test(int eventType)
        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator = new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7);
        BaseSecantSolver rootSolver = new PegasusSolver(e, e);
        EventHandler evt1 = new Event(0, eventType);
        EventHandler evt2 = new Event(1, eventType);
        integrator.addEventHandler(evt1, 0.1, e, 999, rootSolver);
        integrator.addEventHandler(evt2, 0.1, e, 999, rootSolver);
        double t = 0.0;
        double tEnd = 10.0;
        double[] y = {0.0, 0.0};
        List<Double> events1 = new ArrayList<Double>();
        List<Double> events2 = new ArrayList<Double>();
        while (t < tEnd) {
            t = integrator.integrate(this, t, y, tEnd, y);
            //System.out.println("t=" + t + ",\t\ty=[" + y[0] + "," + y[1] + "]");


            if (y[0] >= 1.0) {
                y[0] = 0.0;
                events1.add(t);

View Full Code Here

            public void computeDerivatives(double t, double[] y, double[] yDot) {
                yDot[0] = 1.0;
            }
        };


        DormandPrince853Integrator integrator = new DormandPrince853Integrator(0.001, 1000, 1.0e-14, 1.0e-14);
        integrator.addEventHandler(new ResettingEvent(10.99), 0.1, 1.0e-9, 1000);
        integrator.addEventHandler(new ResettingEvent(11.01), 0.1, 1.0e-9, 1000);
        integrator.setInitialStepSize(3.0);


        double target = 30.0;
        double[] y = new double[1];
        double tEnd = integrator.integrate(equation, 0.0, y, target, y);
        Assert.assertEquals(target, tEnd, 1.0e-10);
        Assert.assertEquals(32.0, y[0], 1.0e-10);


    }

View Full Code Here

        throws DimensionMismatchException, NumberIsTooSmallException,
               MaxCountExceededException, NoBracketingException {
        double e = 1e-15;
        FirstOrderIntegrator integrator;
        integrator = (integratorType == 1)
                     ? new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7)
                     : new GraggBulirschStoerIntegrator(e, 100.0, 1e-7, 1e-7);
        PegasusSolver rootSolver = new PegasusSolver(e, e);
        integrator.addEventHandler(new Event(), 0.1, e, 1000, rootSolver);
        double t0 = 6.0;
        double tEnd = 10.0;

View Full Code Here

0 1 2 3 4 5 6 7 8 9

TOP

Related Classes of org.apache.commons.math3.ode.nonstiff.DormandPrince853Integrator

org.apache.commons.math3.analysis.differentiation.DerivativeStructure

org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction

org.apache.commons.math3.analysis.function.HarmonicOscillator

org.apache.commons.math3.analysis.function.Sin

org.apache.commons.math3.analysis.function.Sinc

org.apache.commons.math3.analysis.MultivariateFunction

org.apache.commons.math3.analysis.QuinticFunction

org.apache.commons.math3.analysis.solvers.BrentSolver

org.apache.commons.math3.analysis.UnivariateFunction

org.apache.commons.math3.complex.Complex

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.