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

Class EmbeddedRungeKuttaIntegrator

  • All Implemented Interfaces:
    FirstOrderIntegrator, ODEIntegrator
    Direct Known Subclasses:
    DormandPrince54Integrator, DormandPrince853Integrator, HighamHall54Integrator
    public abstract class EmbeddedRungeKuttaIntegrator
extends AdaptiveStepsizeIntegrator
    This class implements the common part of all embedded Runge-Kutta integrators for Ordinary Differential Equations.

    These methods are embedded explicit Runge-Kutta methods with two sets of coefficients allowing to estimate the error, their Butcher arrays are as follows : 

        0  |
   c2  | a21
   c3  | a31  a32
   ... |        ...
   cs  | as1  as2  ...  ass-1
       |--------------------------
       |  b1   b2  ...   bs-1  bs
       |  b'1  b'2 ...   b's-1 b's

    In fact, we rather use the array defined by ej = bj - b'j to compute directly the error rather than computing two estimates and then comparing them.

    Some methods are qualified as fsal (first same as last) methods. This means the last evaluation of the derivatives in one step is the same as the first in the next step. Then, this evaluation can be reused from one step to the next one and the cost of such a method is really s-1 evaluations despite the method still has s stages. This behaviour is true only for successful steps, if the step is rejected after the error estimation phase, no evaluation is saved. For an fsal method, we have cs = 1 and asi = bi for all i.

    Since:
    1.2
    Version:
    $Revision: 1073158 $ $Date: 2011-02-21 22:46:52 +0100 (lun. 21 févr. 2011) $

    • Constructor Detail

      • EmbeddedRungeKuttaIntegrator

        protected EmbeddedRungeKuttaIntegrator​(java.lang.String name,
                                       boolean fsal,
                                       double[] c,
                                       double[][] a,
                                       double[] b,
                                       org.apache.commons.math.ode.nonstiff.RungeKuttaStepInterpolator prototype,
                                       double minStep,
                                       double maxStep,
                                       double scalAbsoluteTolerance,
                                       double scalRelativeTolerance)
        Build a Runge-Kutta integrator with the given Butcher array.
        Parameters:
        name - name of the method
        fsal - indicate that the method is an fsal
        c - time steps from Butcher array (without the first zero)
        a - internal weights from Butcher array (without the first empty row)
        b - propagation weights for the high order method from Butcher array
        prototype - prototype of the step interpolator to use
        minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this
        maxStep - maximal step (must be positive even for backward integration)
        scalAbsoluteTolerance - allowed absolute error
        scalRelativeTolerance - allowed relative error

      • EmbeddedRungeKuttaIntegrator

        protected EmbeddedRungeKuttaIntegrator​(java.lang.String name,
                                       boolean fsal,
                                       double[] c,
                                       double[][] a,
                                       double[] b,
                                       org.apache.commons.math.ode.nonstiff.RungeKuttaStepInterpolator prototype,
                                       double minStep,
                                       double maxStep,
                                       double[] vecAbsoluteTolerance,
                                       double[] vecRelativeTolerance)
        Build a Runge-Kutta integrator with the given Butcher array.
        Parameters:
        name - name of the method
        fsal - indicate that the method is an fsal
        c - time steps from Butcher array (without the first zero)
        a - internal weights from Butcher array (without the first empty row)
        b - propagation weights for the high order method from Butcher array
        prototype - prototype of the step interpolator to use
        minStep - minimal step (must be positive even for backward integration), the last step can be smaller than this
        maxStep - maximal step (must be positive even for backward integration)
        vecAbsoluteTolerance - allowed absolute error
        vecRelativeTolerance - allowed relative error

    • Method Detail

      • getOrder

        public abstract int getOrder()
        Get the order of the method.
        Returns:
        order of the method

      • getSafety

        public double getSafety()
        Get the safety factor for stepsize control.
        Returns:
        safety factor

      • setSafety

        public void setSafety​(double safety)
        Set the safety factor for stepsize control.
        Parameters:
        safety - safety factor

      • integrate

        public double integrate​(FirstOrderDifferentialEquations equations,
                        double t0,
                        double[] y0,
                        double t,
                        double[] y)
                 throws DerivativeException,
                        IntegratorException
        Integrate the differential equations up to the given time.

        This method solves an Initial Value Problem (IVP).

        Since this method stores some internal state variables made available in its public interface during integration (ODEIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

        Specified by:
        integrate in interface FirstOrderIntegrator
        Specified by:
        integrate in class AdaptiveStepsizeIntegrator
        Parameters:
        equations - differential equations to integrate
        t0 - initial time
        y0 - initial value of the state vector at t0
        t - target time for the integration (can be set to a value smaller than t0 for backward integration)
        y - placeholder where to put the state vector at each successful step (and hence at the end of integration), can be the same object as y0
        Returns:
        stop time, will be the same as target time if integration reached its target, but may be different if some EventHandler stops it at some point.
        Throws:
        DerivativeException - this exception is propagated to the caller if the underlying user function triggers one
        IntegratorException - if the integrator cannot perform integration

      • getMinReduction

        public double getMinReduction()
        Get the minimal reduction factor for stepsize control.
        Returns:
        minimal reduction factor

      • setMinReduction

        public void setMinReduction​(double minReduction)
        Set the minimal reduction factor for stepsize control.
        Parameters:
        minReduction - minimal reduction factor

      • getMaxGrowth

        public double getMaxGrowth()
        Get the maximal growth factor for stepsize control.
        Returns:
        maximal growth factor

      • setMaxGrowth

        public void setMaxGrowth​(double maxGrowth)
        Set the maximal growth factor for stepsize control.
        Parameters:
        maxGrowth - maximal growth factor

      • estimateError

        protected abstract double estimateError​(double[][] yDotK,
                                        double[] y0,
                                        double[] y1,
                                        double h)
        Compute the error ratio.
        Parameters:
        yDotK - derivatives computed during the first stages
        y0 - estimate of the step at the start of the step
        y1 - estimate of the step at the end of the step
        h - current step
        Returns:
        error ratio, greater than 1 if step should be rejected