org.apache.commons.math3.ode

Class MultistepFieldIntegrator<T extends RealFieldElement<T>>

java.lang.Object

org.apache.commons.math3.ode.AbstractFieldIntegrator<T>

org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator<T>

org.apache.commons.math3.ode.MultistepFieldIntegrator<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

FirstOrderFieldIntegrator<T>

Direct Known Subclasses:

AdamsFieldIntegrator

public abstract class MultistepFieldIntegrator<T extends RealFieldElement<T>>
extends AdaptiveStepsizeFieldIntegrator<T>

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 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:

3.6

See Also:

AdamsBashforthFieldIntegrator, AdamsMoultonFieldIntegrator

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.
int	getNSteps() Get the number of steps of the multistep method (excluding the one being computed).
double	getSafety() Get the safety factor for stepsize control.
FirstOrderFieldIntegrator<T>	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(FirstOrderFieldIntegrator<T> starterIntegrator) Set the starter integrator.

Methods inherited from class org.apache.commons.math3.ode.nonstiff.AdaptiveStepsizeFieldIntegrator

getMaxStep, getMinStep, initializeStep, setInitialStepSize, setStepSizeControl, setStepSizeControl

Methods inherited from class org.apache.commons.math3.ode.AbstractFieldIntegrator

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

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math3.ode.FirstOrderFieldIntegrator

integrate

Method Detail

getStarterIntegrator

public FirstOrderFieldIntegrator<T> getStarterIntegrator()

Get the starter integrator.

Returns:

starter integrator

setStarterIntegrator

public void setStarterIntegrator(FirstOrderFieldIntegrator<T> 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

getNSteps

public int getNSteps()

Get the number of steps of the multistep method (excluding the one being computed).

Returns:

number of steps of the multistep method (excluding the one being computed)