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

Class DormandPrince853Integrator

  • All Implemented Interfaces:
    FirstOrderIntegrator, ODEIntegrator
    public class DormandPrince853Integrator
extends EmbeddedRungeKuttaIntegrator
    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

    • Constructor Detail

      • DormandPrince853Integrator

        public DormandPrince853Integrator​(double minStep,
                                  double maxStep,
                                  double scalAbsoluteTolerance,
                                  double scalRelativeTolerance)
        Simple constructor. Build an eighth order Dormand-Prince integrator with the given step bounds
        Parameters:
        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

      • DormandPrince853Integrator

        public DormandPrince853Integrator​(double minStep,
                                  double maxStep,
                                  double[] vecAbsoluteTolerance,
                                  double[] vecRelativeTolerance)
        Simple constructor. Build an eighth order Dormand-Prince integrator with the given step bounds
        Parameters:
        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