org.apache.commons.math.ode

Class MultistepIntegrator

java.lang.Object

org.apache.commons.math.ode.AbstractIntegrator

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

org.apache.commons.math.ode.MultistepIntegrator

All Implemented Interfaces:

FirstOrderIntegrator, ODEIntegrator

Direct Known Subclasses:

AdamsIntegrator

public abstract class MultistepIntegrator
extends AdaptiveStepsizeIntegrator

This class is the base class for multistep integrators for Ordinary Differential Equations.

We define scaled derivatives s_i(n) at step n as:

 s1(n) = h y'n for first derivative
 s2(n) = h2/2 y''n for second derivative
 s3(n) = h3/6 y'''n for third derivative
 ...
 sk(n) = hk/k! y(k)n for kth derivative
 

Rather than storing several previous steps separately, this implementation uses the Nordsieck vector with higher degrees scaled derivatives all taken at the same step (y_n, s₁(n) and r_n) where r_n is defined as:

 rn = [ s2(n), s3(n) ... sk(n) ]T
 

(we omit the k index in the notation for clarity)

Multistep integrators with Nordsieck representation are highly sensitive to large step changes because when the step is multiplied by a factor a, the k^th component of the Nordsieck vector is multiplied by a^k and the last components are the least accurate ones. The default max growth factor is therefore set to a quite low value: 2^1/order.

Since:

2.0

See Also:

AdamsBashforthIntegrator, AdamsMoultonIntegrator

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static interface	MultistepIntegrator.NordsieckTransformer Transformer used to convert the first step to Nordsieck representation.

Method Summary

Modifier and Type	Method and Description
double	getMaxGrowth() Get the maximal growth factor for stepsize control.
double	getMinReduction() Get the minimal reduction factor for stepsize control.
double	getSafety() Get the safety factor for stepsize control.
ODEIntegrator	getStarterIntegrator() Get the starter integrator.
void	setMaxGrowth(double maxGrowth) Set the maximal growth factor for stepsize control.
void	setMinReduction(double minReduction) Set the minimal reduction factor for stepsize control.
void	setSafety(double safety) Set the safety factor for stepsize control.
void	setStarterIntegrator(FirstOrderIntegrator starterIntegrator) Set the starter integrator.

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

getCurrentStepStart, getMaxStep, getMinStep, initializeStep, integrate, 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

Method Detail

getStarterIntegrator

public ODEIntegrator getStarterIntegrator()

Get the starter integrator.

Returns:

starter integrator

setStarterIntegrator

public void setStarterIntegrator(FirstOrderIntegrator starterIntegrator)

Set the starter integrator.

The various step and event handlers for this starter integrator will be managed automatically by the multi-step integrator. Any user configuration for these elements will be cleared before use.

Parameters:

starterIntegrator - starter integrator

getMinReduction

public double getMinReduction()

Get the minimal reduction factor for stepsize control.

Returns:

minimal reduction factor

setMinReduction

public void setMinReduction(double minReduction)

Set the minimal reduction factor for stepsize control.

Parameters:

minReduction - minimal reduction factor

getMaxGrowth

public double getMaxGrowth()

Get the maximal growth factor for stepsize control.

Returns:

maximal growth factor

setMaxGrowth

public void setMaxGrowth(double maxGrowth)

Set the maximal growth factor for stepsize control.

Parameters:

maxGrowth - maximal growth factor

getSafety

public double getSafety()

Get the safety factor for stepsize control.

Returns:

safety factor

setSafety

public void setSafety(double safety)

Set the safety factor for stepsize control.

Parameters:

safety - safety factor