Package org.hipparchus.ode.nonstiff.interpolators

Class ThreeEighthesStateInterpolator

java.lang.Object

org.hipparchus.ode.sampling.AbstractODEStateInterpolator

org.hipparchus.ode.nonstiff.interpolators.RungeKuttaStateInterpolator

org.hipparchus.ode.nonstiff.interpolators.ThreeEighthesStateInterpolator

All Implemented Interfaces:

Serializable, ODEStateInterpolator

public class ThreeEighthesStateInterpolator
extends RungeKuttaStateInterpolator

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:

ThreeEighthesIntegrator, Serialized Form

Field Summary

Fields inherited from class org.hipparchus.ode.nonstiff.interpolators.RungeKuttaStateInterpolator

yDotK

Constructor Summary

Constructors

Constructor	Description
ThreeEighthesStateInterpolator(boolean forward, double[][] yDotK, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, ODEStateAndDerivative softPreviousState, ODEStateAndDerivative softCurrentState, EquationsMapper mapper)	Simple constructor.

Method Summary

Modifier and Type	Method	Description
protected ODEStateAndDerivative	computeInterpolatedStateAndDerivatives(EquationsMapper mapper, double time, double theta, double thetaH, double oneMinusThetaH)	Compute the state and derivatives at the interpolated time.
protected ThreeEighthesStateInterpolator	create(boolean newForward, double[][] newYDotK, ODEStateAndDerivative newGlobalPreviousState, ODEStateAndDerivative newGlobalCurrentState, ODEStateAndDerivative newSoftPreviousState, ODEStateAndDerivative newSoftCurrentState, EquationsMapper newMapper)	Create a new instance.

Methods inherited from class org.hipparchus.ode.nonstiff.interpolators.RungeKuttaStateInterpolator

create, currentStateLinearCombination, derivativeLinearCombination, previousStateLinearCombination

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

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 Detail

ThreeEighthesStateInterpolator

public ThreeEighthesStateInterpolator(boolean forward,
                                      double[][] yDotK,
                                      ODEStateAndDerivative globalPreviousState,
                                      ODEStateAndDerivative globalCurrentState,
                                      ODEStateAndDerivative softPreviousState,
                                      ODEStateAndDerivative softCurrentState,
                                      EquationsMapper mapper)

Simple constructor.

Parameters:

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 ThreeEighthesStateInterpolator create(boolean newForward,
                                                double[][] newYDotK,
                                                ODEStateAndDerivative newGlobalPreviousState,
                                                ODEStateAndDerivative newGlobalCurrentState,
                                                ODEStateAndDerivative newSoftPreviousState,
                                                ODEStateAndDerivative newSoftCurrentState,
                                                EquationsMapper newMapper)

Create a new instance.

Specified by:

create in class RungeKuttaStateInterpolator

Parameters:

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 ODEStateAndDerivative computeInterpolatedStateAndDerivatives(EquationsMapper mapper,
                                                                       double time,
                                                                       double theta,
                                                                       double thetaH,
                                                                       double 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 AbstractODEStateInterpolator

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