org.apache.commons.math.ode.nonstiff

Class AdamsIntegrator

java.lang.Object

org.apache.commons.math.ode.AbstractIntegrator

org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator

org.apache.commons.math.ode.MultistepIntegrator

org.apache.commons.math.ode.nonstiff.AdamsIntegrator

All Implemented Interfaces:

FirstOrderIntegrator, ODEIntegrator

Direct Known Subclasses:

AdamsBashforthIntegrator, AdamsMoultonIntegrator

public abstract class AdamsIntegrator
extends MultistepIntegrator

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

Since:

2.0

Nested Class Summary

Nested classes/interfaces inherited from class org.apache.commons.math.ode.MultistepIntegrator

MultistepIntegrator.NordsieckTransformer

Constructor Summary

Constructors

Constructor and Description
AdamsIntegrator(java.lang.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(java.lang.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 prameters.

Method Summary

Modifier and Type	Method and Description
abstract double	integrate(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y) 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.apache.commons.math.ode.MultistepIntegrator

getMaxGrowth, getMinReduction, getSafety, getStarterIntegrator, setMaxGrowth, setMinReduction, setSafety, setStarterIntegrator

Methods inherited from class org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator

getCurrentStepStart, getMaxStep, getMinStep, initializeStep, setInitialStepSize

Methods inherited from class org.apache.commons.math.ode.AbstractIntegrator

addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEventHandlers, getMaxEvaluations, getName, getStepHandlers, setMaxEvaluations

Methods inherited from class java.lang.Object

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

Constructor Detail

AdamsIntegrator

public AdamsIntegrator(java.lang.String name,
                       int nSteps,
                       int order,
                       double minStep,
                       double maxStep,
                       double scalAbsoluteTolerance,
                       double scalRelativeTolerance)
                throws java.lang.IllegalArgumentException

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

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 (must be positive even for backward integration), the last step can be smaller than this

maxStep - maximal step (must be positive even for backward integration)

scalAbsoluteTolerance - allowed absolute error

scalRelativeTolerance - allowed relative error

Throws:

java.lang.IllegalArgumentException - if order is 1 or less

AdamsIntegrator

public AdamsIntegrator(java.lang.String name,
                       int nSteps,
                       int order,
                       double minStep,
                       double maxStep,
                       double[] vecAbsoluteTolerance,
                       double[] vecRelativeTolerance)
                throws java.lang.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 (must be positive even for backward integration), the last step can be smaller than this

maxStep - maximal step (must be positive even for backward integration)

vecAbsoluteTolerance - allowed absolute error

vecRelativeTolerance - allowed relative error

Throws:

java.lang.IllegalArgumentException - if order is 1 or less

Method Detail

integrate

public abstract double integrate(FirstOrderDifferentialEquations equations,
                                 double t0,
                                 double[] y0,
                                 double t,
                                 double[] y)
                          throws DerivativeException,
                                 IntegratorException

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.

Specified by:

integrate in interface FirstOrderIntegrator

Specified by:

integrate in class AdaptiveStepsizeIntegrator

Parameters:

equations - differential equations to integrate

t0 - initial time

y0 - initial value of the state vector at t0

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

y - placeholder where to put the state vector at each successful step (and hence at the end of integration), can be the same object as y0

Returns:

stop time, will be the same as target time if integration reached its target, but may be different if some EventHandler stops it at some point.

Throws:

DerivativeException - this exception is propagated to the caller if the underlying user function triggers one

IntegratorException - if the integrator cannot perform integration

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)