Class DormandPrince54Integrator

All Implemented Interfaces:
FirstOrderIntegrator, ODEIntegrator

public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator
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
 

Since:
1.2
  • Field Details

    • METHOD_NAME

      private static final String METHOD_NAME
      Integrator method name.
      See Also:
    • STATIC_C

      private static final double[] STATIC_C
      Time steps Butcher array.
    • STATIC_A

      private static final double[][] STATIC_A
      Internal weights Butcher array.
    • STATIC_B

      private static final double[] STATIC_B
      Propagation weights Butcher array.
    • E1

      private static final double E1
      Error array, element 1.
      See Also:
    • E3

      private static final double E3
      Error array, element 3.
      See Also:
    • E4

      private static final double E4
      Error array, element 4.
      See Also:
    • E5

      private static final double E5
      Error array, element 5.
      See Also:
    • E6

      private static final double E6
      Error array, element 6.
      See Also:
    • E7

      private static final double E7
      Error array, element 7.
      See Also:
  • Constructor Details

    • DormandPrince54Integrator

      public DormandPrince54Integrator(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
    • DormandPrince54Integrator

      public DormandPrince54Integrator(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

    • 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