Package 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

Constructor Summary

Constructors

Constructor	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	Description
protected abstract double	errorEstimation(double[] previousState, double predictedTime, double[] predictedState, double[] predictedScaled, RealMatrix predictedNordsieck)	Estimate error.
protected abstract org.hipparchus.ode.nonstiff.AdamsStateInterpolator	finalizeStep(double stepSize, double[] predictedState, double[] predictedScaled, Array2DRowRealMatrix predictedNordsieck, boolean isForward, ODEStateAndDerivative globalPreviousState, ODEStateAndDerivative globalCurrentState, EquationsMapper equationsMapper)	Finalize the step.
protected Array2DRowRealMatrix	initializeHighOrderDerivatives(double h, double[] t, double[][] y, double[][] yDot)	Initialize the high order scaled derivatives at step start.
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

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

Methods inherited from class org.hipparchus.ode.AbstractIntegrator

acceptStep, addEventDetector, addStepEndHandler, addStepHandler, clearEventDetectors, clearStepEndHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEquations, getEvaluations, getEvaluationsCounter, getEventDetectors, getMaxEvaluations, getName, getStepEndHandlers, getStepHandlers, getStepSize, getStepStart, incrementEvaluations, 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

Constructor Details

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 Details

integrate

public 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: \[ r_{n+1} = (s_1(n) - s_1(n+1)) P^{-1} u + P^{-1} A P r_n \] 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: \[ r_{n+1} = (s_1(n) - s_1(n+1)) P^{-1} u + P^{-1} A P r_n \] 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)

errorEstimation

protected abstract double errorEstimation(double[] previousState,
 double predictedTime,
 double[] predictedState,
 double[] predictedScaled,
 RealMatrix predictedNordsieck)

Estimate error.

Parameters:

previousState - state vector at step start

predictedTime - time at step end

predictedState - predicted state vector at step end

predictedScaled - predicted value of the scaled derivatives at step end

predictedNordsieck - predicted value of the Nordsieck vector at step end

Returns:

estimated normalized local discretization error

Since:

2.0

finalizeStep

protected abstract org.hipparchus.ode.nonstiff.AdamsStateInterpolator finalizeStep(double stepSize,
 double[] predictedState,
 double[] predictedScaled,
 Array2DRowRealMatrix predictedNordsieck,
 boolean isForward,
 ODEStateAndDerivative globalPreviousState,
 ODEStateAndDerivative globalCurrentState,
 EquationsMapper equationsMapper)

Finalize the step.

Parameters:

stepSize - step size used in the scaled and Nordsieck arrays

predictedState - predicted state at end of step

predictedScaled - predicted first scaled derivative

predictedNordsieck - predicted Nordsieck vector

isForward - integration direction indicator

globalPreviousState - start of the global step

globalCurrentState - end of the global step

equationsMapper - mapper for ODE equations primary and secondary components

Returns:

step interpolator

Since:

2.0