org.apache.commons.math3.ode.nonstiff

• ### Nested classes/interfaces inherited from class org.apache.commons.math3.ode.MultistepIntegrator

MultistepIntegrator.NordsieckTransformer

• ### Fields inherited from class org.apache.commons.math3.ode.MultistepIntegrator

nordsieck, scaled
• ### Fields inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator

mainSetDimension, scalAbsoluteTolerance, scalRelativeTolerance, vecAbsoluteTolerance, vecRelativeTolerance
• ### Fields inherited from class org.apache.commons.math3.ode.AbstractIntegrator

isLastStep, resetOccurred, stepHandlers, stepSize, stepStart
• ### 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

Methods
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 void integrate(ExpandableStatefulODE equations, double t)
Integrate a set of 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.math3.ode.MultistepIntegrator

computeStepGrowShrinkFactor, getMaxGrowth, getMinReduction, getSafety, getStarterIntegrator, setMaxGrowth, setMinReduction, setSafety, setStarterIntegrator, start
• ### Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeIntegrator

filterStep, getCurrentStepStart, getMaxStep, getMinStep, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepSizeControl, setStepSizeControl
• ### Methods inherited from class org.apache.commons.math3.ode.AbstractIntegrator

acceptStep, addEventHandler, addEventHandler, addStepHandler, clearEventHandlers, clearStepHandlers, computeDerivatives, getCurrentSignedStepsize, getEvaluations, getEvaluationsCounter, getEventHandlers, getExpandable, getMaxEvaluations, getName, getStepHandlers, initIntegration, integrate, setEquations, setMaxEvaluations, setStateInitialized
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

public AdamsIntegrator(String name,
int nSteps,
int order,
double minStep,
double maxStep,
double scalAbsoluteTolerance,
double scalRelativeTolerance)
throws NumberIsTooSmallException
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:
NumberIsTooSmallException - if order is 1 or less

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 void integrate(ExpandableStatefulODE equations,
double t)
throws NumberIsTooSmallException,
DimensionMismatchException,
MaxCountExceededException,
NoBracketingException
Integrate a set of differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

The set of differential equations is composed of a main set, which can be extended by some sets of secondary equations. The set of equations must be already set up with initial time and partial states. At integration completion, the final time and partial states will be available in the same object.

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

Specified by:
integrate in class AdaptiveStepsizeIntegrator
Parameters:
equations - complete set of differential equations to integrate
t - target time for the integration (can be set to a value smaller than t0 for backward integration)
Throws:
NumberIsTooSmallException - if integration step is too small
DimensionMismatchException - if the dimension of the complete state does not match the complete equations sets dimension
MaxCountExceededException - if the number of functions evaluations is exceeded
NoBracketingException - if the location of an event cannot be bracketed
• #### 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 ... hk/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 rn part.

Parameters:
highOrder - high order scaled derivatives (h2/2 y'', ... hk/k! y(k))
Returns:
updated high order derivatives
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'', ... hk/k! y(k))
updateHighOrderDerivativesPhase1(Array2DRowRealMatrix)