Package org.hipparchus.ode.nonstiff

Class DormandPrince54FieldIntegrator<T extends RealFieldElement<T>>

  • Type Parameters:
    T - the type of the field elements
    All Implemented Interfaces:
    FieldODEIntegrator<T>, FieldButcherArrayProvider<T>
    public class DormandPrince54FieldIntegrator<T extends RealFieldElement<T>>
extends EmbeddedRungeKuttaFieldIntegrator<T>
    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

    • Constructor Detail

      • DormandPrince54FieldIntegrator

        public DormandPrince54FieldIntegrator​(Field<T> field,
                                      double minStep,
                                      double maxStep,
                                      double scalAbsoluteTolerance,
                                      double scalRelativeTolerance)
        Simple constructor. Build a fifth order Dormand-Prince integrator with the given step bounds
        Parameters:
        field - field to which the time and state vector elements belong
        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

      • DormandPrince54FieldIntegrator

        public DormandPrince54FieldIntegrator​(Field<T> field,
                                      double minStep,
                                      double maxStep,
                                      double[] vecAbsoluteTolerance,
                                      double[] vecRelativeTolerance)
        Simple constructor. Build a fifth order Dormand-Prince integrator with the given step bounds
        Parameters:
        field - field to which the time and state vector elements belong
        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 Detail

      • getC

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

      • getA

        public T[][] 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 T[] 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.DormandPrince54FieldStateInterpolator<T> createInterpolator​(boolean forward,
                                                                                                  T[][] yDotK,
                                                                                                  FieldODEStateAndDerivative<T> globalPreviousState,
                                                                                                  FieldODEStateAndDerivative<T> globalCurrentState,
                                                                                                  FieldEquationsMapper<T> mapper)
        Create an interpolator.
        Specified by:
        createInterpolator in class EmbeddedRungeKuttaFieldIntegrator<T extends RealFieldElement<T>>
        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

      • estimateError

        protected T estimateError​(T[][] yDotK,
                          T[] y0,
                          T[] y1,
                          T h)
        Compute the error ratio.
        Specified by:
        estimateError in class EmbeddedRungeKuttaFieldIntegrator<T extends RealFieldElement<T>>
        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