org.apache.commons.math3.ode.nonstiff

Class ThreeEighthesFieldStepInterpolator<T extends RealFieldElement<T>>

java.lang.Object

org.apache.commons.math3.ode.sampling.AbstractFieldStepInterpolator<T>

org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldStepInterpolator<T>

org.apache.commons.math3.ode.nonstiff.ThreeEighthesFieldStepInterpolator<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

FieldStepInterpolator<T>

 class ThreeEighthesFieldStepInterpolator<T extends RealFieldElement<T>>
extends RungeKuttaFieldStepInterpolator<T>

This class implements a step interpolator for the 3/8 fourth order Runge-Kutta integrator.

This interpolator allows to compute dense output inside the last step computed. The interpolation equation is consistent with the integration scheme :

• Using reference point at step start:
  y(t_n + θ h) = y (t_n) + θ (h/8) [ (8 - 15 θ + 8 θ²) y'₁ + 3 * (15 θ - 12 θ²) y'₂ + 3 θ y'₃ + (-3 θ + 4 θ²) y'₄ ]
• Using reference point at step end:
  y(t_n + θ h) = y (t_n + h) - (1 - θ) (h/8) [(1 - 7 θ + 8 θ²) y'₁ + 3 (1 + θ - 4 θ²) y'₂ + 3 (1 + θ) y'₃ + (1 + θ + 4 θ²) y'₄ ]

where θ belongs to [0 ; 1] and where y'₁ to y'₄ are the four evaluations of the derivatives already computed during the step.

Since:

3.6

See Also:

ThreeEighthesFieldIntegrator

Constructor Summary

Constructors

Constructor and Description
ThreeEighthesFieldStepInterpolator(Field<T> field, boolean forward, T[][] yDotK, FieldODEStateAndDerivative<T> globalPreviousState, FieldODEStateAndDerivative<T> globalCurrentState, FieldODEStateAndDerivative<T> softPreviousState, FieldODEStateAndDerivative<T> softCurrentState, FieldEquationsMapper<T> mapper) Simple constructor.

Method Summary

Methods

Modifier and Type	Method and Description
protected FieldODEStateAndDerivative<T>	computeInterpolatedStateAndDerivatives(FieldEquationsMapper<T> mapper, T time, T theta, T thetaH, T oneMinusThetaH) Compute the state and derivatives at the interpolated time.
protected ThreeEighthesFieldStepInterpolator<T>	create(Field<T> newField, boolean newForward, T[][] newYDotK, FieldODEStateAndDerivative<T> newGlobalPreviousState, FieldODEStateAndDerivative<T> newGlobalCurrentState, FieldODEStateAndDerivative<T> newSoftPreviousState, FieldODEStateAndDerivative<T> newSoftCurrentState, FieldEquationsMapper<T> newMapper) Create a new instance.

Methods inherited from class org.apache.commons.math3.ode.nonstiff.RungeKuttaFieldStepInterpolator

create, currentStateLinearCombination, derivativeLinearCombination, previousStateLinearCombination

Methods inherited from class org.apache.commons.math3.ode.sampling.AbstractFieldStepInterpolator

getCurrentState, getGlobalCurrentState, getGlobalPreviousState, getInterpolatedState, getPreviousState, isForward, restrictStep

Methods inherited from class java.lang.Object

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

Constructor Detail

ThreeEighthesFieldStepInterpolator

ThreeEighthesFieldStepInterpolator(Field<T> field,
                                  boolean forward,
                                  T[][] yDotK,
                                  FieldODEStateAndDerivative<T> globalPreviousState,
                                  FieldODEStateAndDerivative<T> globalCurrentState,
                                  FieldODEStateAndDerivative<T> softPreviousState,
                                  FieldODEStateAndDerivative<T> softCurrentState,
                                  FieldEquationsMapper<T> mapper)

Simple constructor.

Parameters:

field - field to which the time and state vector elements belong

forward - integration direction indicator

yDotK - slopes at the intermediate points

globalPreviousState - start of the global step

globalCurrentState - end of the global step

softPreviousState - start of the restricted step

softCurrentState - end of the restricted step

mapper - equations mapper for the all equations

Method Detail

create

protected ThreeEighthesFieldStepInterpolator<T> create(Field<T> newField,
                                           boolean newForward,
                                           T[][] newYDotK,
                                           FieldODEStateAndDerivative<T> newGlobalPreviousState,
                                           FieldODEStateAndDerivative<T> newGlobalCurrentState,
                                           FieldODEStateAndDerivative<T> newSoftPreviousState,
                                           FieldODEStateAndDerivative<T> newSoftCurrentState,
                                           FieldEquationsMapper<T> newMapper)

Create a new instance.

Specified by:

create in class RungeKuttaFieldStepInterpolator<T extends RealFieldElement<T>>

Parameters:

newField - field to which the time and state vector elements belong

newForward - integration direction indicator

newYDotK - slopes at the intermediate points

newGlobalPreviousState - start of the global step

newGlobalCurrentState - end of the global step

newSoftPreviousState - start of the restricted step

newSoftCurrentState - end of the restricted step

newMapper - equations mapper for the all equations

Returns:

a new instance

computeInterpolatedStateAndDerivatives

protected FieldODEStateAndDerivative<T> computeInterpolatedStateAndDerivatives(FieldEquationsMapper<T> mapper,
                                                                   T time,
                                                                   T theta,
                                                                   T thetaH,
                                                                   T oneMinusThetaH)

Compute the state and derivatives at the interpolated time. This is the main processing method that should be implemented by the derived classes to perform the interpolation.

Specified by:

computeInterpolatedStateAndDerivatives in class AbstractFieldStepInterpolator<T extends RealFieldElement<T>>

Parameters:

mapper - mapper for ODE equations primary and secondary components

time - interpolation time

theta - normalized interpolation abscissa within the step (theta is zero at the previous time step and one at the current time step)

thetaH - time gap between the previous time and the interpolated time

oneMinusThetaH - time gap between the interpolated time and the current time

Returns:

interpolated state and derivatives