Package org.hipparchus.ode.nonstiff.interpolators

Class ThreeEighthesFieldStateInterpolator<T extends CalculusFieldElement<T>>

java.lang.Object

org.hipparchus.ode.sampling.AbstractFieldODEStateInterpolator<T>

org.hipparchus.ode.nonstiff.interpolators.RungeKuttaFieldStateInterpolator<T>

org.hipparchus.ode.nonstiff.interpolators.ThreeEighthesFieldStateInterpolator<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

FieldODEStateInterpolator<T>

public class ThreeEighthesFieldStateInterpolator<T extends CalculusFieldElement<T>>
extends RungeKuttaFieldStateInterpolator<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.

See Also:

• ThreeEighthesFieldIntegrator

Constructor Summary

Constructors

Constructor	Description
ThreeEighthesFieldStateInterpolator(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

Modifier and Type	Method	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 ThreeEighthesFieldStateInterpolator<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.hipparchus.ode.nonstiff.interpolators.RungeKuttaFieldStateInterpolator

create, currentStateLinearCombination, derivativeLinearCombination, previousStateLinearCombination

Methods inherited from class org.hipparchus.ode.sampling.AbstractFieldODEStateInterpolator

getCurrentState, getGlobalCurrentState, getGlobalPreviousState, getInterpolatedState, getMapper, getPreviousState, isCurrentStateInterpolated, isForward, isPreviousStateInterpolated, restrictStep

Methods inherited from class java.lang.Object

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

Constructor Details

ThreeEighthesFieldStateInterpolator

public ThreeEighthesFieldStateInterpolator(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 Details

create

protected ThreeEighthesFieldStateInterpolator<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 RungeKuttaFieldStateInterpolator<T extends CalculusFieldElement<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 AbstractFieldODEStateInterpolator<T extends CalculusFieldElement<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