org.apache.commons.math.ode
Class HighamHall54Integrator

java.lang.Object
  extended by org.apache.commons.math.ode.AdaptiveStepsizeIntegrator
      extended by org.apache.commons.math.ode.EmbeddedRungeKuttaIntegrator
          extended by org.apache.commons.math.ode.HighamHall54Integrator
All Implemented Interfaces:
FirstOrderIntegrator

public class HighamHall54Integrator
extends EmbeddedRungeKuttaIntegrator

This class implements the 5(4) Higham and Hall integrator for Ordinary Differential Equations.

This integrator is an embedded Runge-Kutta integrator of order 5(4) used in local extrapolation mode (i.e. the solution is computed using the high order formula) with stepsize control (and automatic step initialization) and continuous output. This method uses 7 functions evaluations per step.

Since:
1.2
Version:
$Revision: 620312 $ $Date: 2008-02-10 12:28:59 -0700 (Sun, 10 Feb 2008) $

Field Summary
private static java.lang.String methodName
          Integrator method name.
private static double[][] staticA
          Internal weights Butcher array.
private static double[] staticB
          Propagation weights Butcher array.
private static double[] staticC
          Time steps Butcher array.
private static double[] staticE
          Error weights Butcher array.
 
Fields inherited from class org.apache.commons.math.ode.AdaptiveStepsizeIntegrator
handler, scalAbsoluteTolerance, scalRelativeTolerance, stepSize, stepStart, switchesHandler, vecAbsoluteTolerance, vecRelativeTolerance
 
Constructor Summary
HighamHall54Integrator(double minStep, double maxStep, double[] vecAbsoluteTolerance, double[] vecRelativeTolerance)
          Simple constructor.
HighamHall54Integrator(double minStep, double maxStep, double scalAbsoluteTolerance, double scalRelativeTolerance)
          Simple constructor.
 
Method Summary
protected  double estimateError(double[][] yDotK, double[] y0, double[] y1, double h)
          Compute the error ratio.
 java.lang.String getName()
          Get the name of the method.
 int getOrder()
          Get the order of the method.
 
Methods inherited from class org.apache.commons.math.ode.EmbeddedRungeKuttaIntegrator
getMaxGrowth, getMinReduction, getSafety, integrate, setMaxGrowth, setMinReduction, setSafety
 
Methods inherited from class org.apache.commons.math.ode.AdaptiveStepsizeIntegrator
addSwitchingFunction, filterStep, getCurrentSignedStepsize, getCurrentStepStart, getMaxStep, getMinStep, getStepHandler, initializeStep, resetInternalState, sanityChecks, setInitialStepSize, setStepHandler
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

methodName

private static final java.lang.String methodName
Integrator method name.

See Also:
Constant Field Values

staticC

private static final double[] staticC
Time steps Butcher array.


staticA

private static final double[][] staticA
Internal weights Butcher array.


staticB

private static final double[] staticB
Propagation weights Butcher array.


staticE

private static final double[] staticE
Error weights Butcher array.

Constructor Detail

HighamHall54Integrator

public HighamHall54Integrator(double minStep,
                              double maxStep,
                              double scalAbsoluteTolerance,
                              double scalRelativeTolerance)
Simple constructor. Build a fifth order Higham and Hall integrator with the given step bounds

Parameters:
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

HighamHall54Integrator

public HighamHall54Integrator(double minStep,
                              double maxStep,
                              double[] vecAbsoluteTolerance,
                              double[] vecRelativeTolerance)
Simple constructor. Build a fifth order Higham and Hall integrator with the given step bounds

Parameters:
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
Method Detail

getName

public java.lang.String getName()
Get the name of the method.

Specified by:
getName in interface FirstOrderIntegrator
Specified by:
getName in class EmbeddedRungeKuttaIntegrator
Returns:
name of the method

getOrder

public int getOrder()
Get the order of the method.

Specified by:
getOrder in class EmbeddedRungeKuttaIntegrator
Returns:
order of the method

estimateError

protected double estimateError(double[][] yDotK,
                               double[] y0,
                               double[] y1,
                               double h)
Compute the error ratio.

Specified by:
estimateError in class EmbeddedRungeKuttaIntegrator
Parameters:
yDotK - derivatives computed during the first stages
y0 - estimate of the step at the start of the step
y1 - estimate of the step at the end of the step
h - current step
Returns:
error ratio, greater than 1 if step should be rejected