org.apache.commons.math.ode
Class MultistepIntegrator

java.lang.Object
  extended by org.apache.commons.math.ode.AbstractIntegrator
      extended by org.apache.commons.math.ode.nonstiff.AdaptiveStepsizeIntegrator
          extended by 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 si(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 (yn, s1(n) and rn) where rn 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 kth component of the Nordsieck vector is multiplied by ak and the last components are the least accurate ones. The default max growth factor is therefore set to a quite low value: 21/order.

Since:
2.0
See Also:
AdamsBashforthIntegrator, AdamsMoultonIntegrator

Nested Class Summary
static interface MultistepIntegrator.NordsieckTransformer
          Transformer used to convert the first step to Nordsieck representation.
 
Method Summary
 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


jHepWork 3.0 ©