org.apache.commons.math3.ode.nonstiff

## Class DormandPrince54FieldIntegrator<T extends RealFieldElement<T>>

- java.lang.Object
- - org.apache.commons.math3.ode.AbstractFieldIntegrator<T>
  - - org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator<T>
    - - org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaFieldIntegrator<T>
      - - org.apache.commons.math3.ode.nonstiff.DormandPrince54FieldIntegrator<T>

- Type Parameters:
    `T` - the type of the field elements
  All Implemented Interfaces:
    FirstOrderFieldIntegrator<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

  Since:
    3.6

- - ### Field Summary

    - ### Fields inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator

      `mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `DormandPrince54FieldIntegrator(Field<T> field, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)` Simple constructor.
    `DormandPrince54FieldIntegrator(Field<T> field, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)` Simple constructor.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `protected org.apache.commons.math3.ode.nonstiff.DormandPrince54FieldStepInterpolator<T>` | `createInterpolator(boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldEquationsMapper<T> mapper)` Create an interpolator.
    `protected T` | `estimateError(T[][] yDotK, T[] y0, T[] y1, T h)` Compute the error ratio.
    `T[][]` | `getA()` Get the internal weights from Butcher array (without the first empty row).
    `T[]` | `getB()` Get the external weights for the high order method from Butcher array.
    `T[]` | `getC()` Get the time steps from Butcher array (without the first zero).
    `int` | `getOrder()` Get the order of the method.

    - ### Methods inherited from class org.apache.commons.math3.ode.nonstiff.EmbeddedRungeKuttaFieldIntegrator

      `fraction, fraction, getMaxGrowth, getMinReduction, getSafety, integrate, setMaxGrowth, setMinReduction, setSafety`

    - ### Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator

      `filterStep, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl`

    - ### Methods inherited from class org.apache.commons.math3.ode.AbstractFieldIntegrator

      `acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEquations, getEvaluations, getEvaluationsCounter, getEventHandlers, getField, getMaxEvaluations, getName, getStepHandlers, getStepSize, getStepStart, initIntegration, isLastStep, resetOccurred, setIsLastStep, setMaxEvaluations, setStateInitialized, setStepSize, setStepStart`

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### 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.apache.commons.math3.ode.nonstiff.DormandPrince54FieldStepInterpolator<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

    - #### getOrder

          public int getOrder()

      Get the order of the method.
      Specified by:
        `getOrder` in class `EmbeddedRungeKuttaFieldIntegrator<T extends RealFieldElement<T>>`
      Returns:
        order of the method

    - #### 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

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