Package org.hipparchus.ode.nonstiff

Class DormandPrince853Integrator

java.lang.Object
org.hipparchus.ode.AbstractIntegrator
org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator
org.hipparchus.ode.nonstiff.EmbeddedRungeKuttaIntegrator
org.hipparchus.ode.nonstiff.DormandPrince853Integrator
All Implemented Interfaces:
ButcherArrayProvider, ExplicitRungeKuttaIntegrator, 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).

  • Field Details

  • Constructor Details

    • DormandPrince853Integrator

      public DormandPrince853Integrator(double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
      Simple constructor. Build a fifth order Dormand-Prince integrator with the given step bounds
      Parameters:
      minStep - minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
      maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
      scalAbsoluteTolerance - allowed absolute error
      scalRelativeTolerance - allowed relative error

    • DormandPrince853Integrator

      public DormandPrince853Integrator(double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
      Simple constructor. Build a fifth order Dormand-Prince integrator with the given step bounds
      Parameters:
      minStep - minimal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
      maxStep - maximal step (sign is irrelevant, regardless of integration direction, forward or backward), the last step can be smaller than this
      vecAbsoluteTolerance - allowed absolute error
      vecRelativeTolerance - allowed relative error

  • Method Details

    • getC

      public double[] getC()
      Get the time steps from Butcher array (without the first zero).
      Returns:
      time steps from Butcher array (without the first zero

    • getA

      public double[][] getA()
      Get the internal weights from Butcher array (without the first empty row).
      Returns:
      internal weights from Butcher array (without the first empty row)

    • getB

      public double[] getB()
      Get the external weights for the high order method from Butcher array.
      Returns:
      external weights for the high order method from Butcher array

    • createInterpolator

      protected org.hipparchus.ode.nonstiff.DormandPrince853StateInterpolator createInterpolator(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper mapper)
      Create an interpolator.
      Specified by:
      createInterpolator in class EmbeddedRungeKuttaIntegrator
      Parameters:
      forward - integration direction indicator
      yDotK - slopes at the intermediate points
      globalPreviousState - start of the global step
      globalCurrentState - end of the global step
      mapper - equations mapper for the all equations
      Returns:
      external weights for the high order method from Butcher array

    • getOrder

      public int getOrder()
      Get the order of the method.
      Specified by:
      getOrder in class EmbeddedRungeKuttaIntegrator
      Returns:
      order of the method

    • estimateError

      protected double estimateError(double[][] yDotK, double[] y0, double[] y1, double h)
      Compute the error ratio.
      Specified by:
      estimateError in class EmbeddedRungeKuttaIntegrator
      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