org.hipparchus.ode.nonstiff

Class AdamsIntegrator

java.lang.Object

org.hipparchus.ode.AbstractIntegrator

org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator

org.hipparchus.ode.MultistepIntegrator

org.hipparchus.ode.nonstiff.AdamsIntegrator

All Implemented Interfaces:

ODEIntegrator

Direct Known Subclasses:

AdamsBashforthIntegrator, AdamsMoultonIntegrator

public abstract class AdamsIntegrator
extends MultistepIntegrator

Base class for Adams-Bashforth and Adams-Moulton integrators.

Field Summary

Fields inherited from class org.hipparchus.ode.MultistepIntegrator

nordsieck, scaled

Fields inherited from class org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator

mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance

Constructor Summary

Constructors

Constructor and Description
AdamsIntegrator(String name, int nSteps, int order, double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance) Build an Adams integrator with the given order and step control parameters.
AdamsIntegrator(String name, int nSteps, int order, double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance) Build an Adams integrator with the given order and step control parameters.

Method Summary

Modifier and Type	Method and Description
protected Array2DRowRealMatrix	initializeHighOrderDerivatives(double h, double[] t, double[][] y, double[][] yDot) Initialize the high order scaled derivatives at step start.
abstract ODEStateAndDerivative	integrate(ExpandableODE equations, ODEState initialState, double finalTime) Integrate the differential equations up to the given time.
Array2DRowRealMatrix	updateHighOrderDerivativesPhase1(Array2DRowRealMatrix highOrder) Update the high order scaled derivatives for Adams integrators (phase 1).
void	updateHighOrderDerivativesPhase2(double[] start, double[] end, Array2DRowRealMatrix highOrder) Update the high order scaled derivatives Adams integrators (phase 2).

Methods inherited from class org.hipparchus.ode.MultistepIntegrator

computeStepGrowShrinkFactor, getMaxGrowth, getMinReduction, getNSteps, getSafety, getStarterIntegrator, rescale, setMaxGrowth, setMinReduction, setSafety, setStarterIntegrator, start

Methods inherited from class org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator

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

Methods inherited from class org.hipparchus.ode.AbstractIntegrator

acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getCurrentStepStart, getEquations, getEvaluations, getEvaluationsCounter, getEventHandlers, 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

Methods inherited from interface org.hipparchus.ode.ODEIntegrator

integrate, integrate

Constructor Detail

AdamsIntegrator

public AdamsIntegrator(String name,
                       int nSteps,
                       int order,
                       double minStep,
                       double maxStep,
                       double scalAbsoluteTolerance,
                       double scalRelativeTolerance)
                throws MathIllegalArgumentException

Build an Adams integrator with the given order and step control parameters.

Parameters:

name - name of the method

nSteps - number of steps of the method excluding the one being computed

order - order of the method

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

Throws:

MathIllegalArgumentException - if order is 1 or less

AdamsIntegrator

public AdamsIntegrator(String name,
                       int nSteps,
                       int order,
                       double minStep,
                       double maxStep,
                       double[] vecAbsoluteTolerance,
                       double[] vecRelativeTolerance)
                throws IllegalArgumentException

Build an Adams integrator with the given order and step control parameters.

Parameters:

name - name of the method

nSteps - number of steps of the method excluding the one being computed

order - order of the method

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

Throws:

IllegalArgumentException - if order is 1 or less

Method Detail

integrate

public abstract ODEStateAndDerivative integrate(ExpandableODE equations,
                                                ODEState initialState,
                                                double finalTime)
                                         throws MathIllegalArgumentException,
                                                MathIllegalStateException

Integrate the differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

Since this method stores some internal state variables made available in its public interface during integration (ODEIntegrator.getCurrentSignedStepsize()), it is not thread-safe.

Parameters:

equations - differential equations to integrate

initialState - initial state (time, primary and secondary state vectors)

finalTime - target time for the integration (can be set to a value smaller than t0 for backward integration)

Returns:

final state, its time will be the same as finalTime if integration reached its target, but may be different if some ODEEventHandler stops it at some point.

Throws:

MathIllegalArgumentException - if integration step is too small

MathIllegalStateException - if the number of functions evaluations is exceeded

initializeHighOrderDerivatives

protected Array2DRowRealMatrix initializeHighOrderDerivatives(double h,
                                                              double[] t,
                                                              double[][] y,
                                                              double[][] yDot)

Initialize the high order scaled derivatives at step start.

Specified by:

initializeHighOrderDerivatives in class MultistepIntegrator

Parameters:

h - step size to use for scaling

t - first steps times

y - first steps states

yDot - first steps derivatives

Returns:

Nordieck vector at first step (h²/2 y''_n, h³/6 y'''_n ... h^k/k! y^(k)_n)

updateHighOrderDerivativesPhase1

public Array2DRowRealMatrix updateHighOrderDerivativesPhase1(Array2DRowRealMatrix highOrder)

Update the high order scaled derivatives for Adams integrators (phase 1).

The complete update of high order derivatives has a form similar to:

 rn+1 = (s1(n) - s1(n+1)) P-1 u + P-1 A P rn
 

this method computes the P^-1 A P r_n part.

Parameters:

highOrder - high order scaled derivatives (h²/2 y'', ... h^k/k! y(k))

Returns:

updated high order derivatives

See Also:

updateHighOrderDerivativesPhase2(double[], double[], Array2DRowRealMatrix)

updateHighOrderDerivativesPhase2

public void updateHighOrderDerivativesPhase2(double[] start,
                                             double[] end,
                                             Array2DRowRealMatrix highOrder)

Update the high order scaled derivatives Adams integrators (phase 2).

The complete update of high order derivatives has a form similar to:

 rn+1 = (s1(n) - s1(n+1)) P-1 u + P-1 A P rn
 

this method computes the (s₁(n) - s₁(n+1)) P^-1 u part.

Phase 1 of the update must already have been performed.

Parameters:

start - first order scaled derivatives at step start

end - first order scaled derivatives at step end

highOrder - high order scaled derivatives, will be modified (h²/2 y'', ... h^k/k! y(k))

See Also:

updateHighOrderDerivativesPhase1(Array2DRowRealMatrix)