org.jscience.mathematics.analysis.ode
Class RungeKuttaIntegrator

java.lang.Object
  org.jscience.mathematics.analysis.ode.RungeKuttaIntegrator

All Implemented Interfaces:

FirstOrderIntegrator, Named

Direct Known Subclasses:

ClassicalRungeKuttaIntegrator, EulerIntegrator, GillIntegrator, MidpointIntegrator, ThreeEighthesIntegrator

public abstract class RungeKuttaIntegrator
extends java.lang.Object
implements FirstOrderIntegrator, Named

This class implements the common part of all fixed step Runge-Kutta integrators for Ordinary Differential Equations.

These methods are explicit Runge-Kutta methods, their Butcher arrays are as follows :

    0  |
   c2  | a21
   c3  | a31  a32
   ... |        ...
   cs  | as1  as2  ...  ass-1
       |--------------------------
       |  b1   b2  ...   bs-1  bs
 

Some methods are qualified as fsal (first same as last) methods. This means the last evaluation of the derivatives in one step is the same as the first in the next step. Then, this evaluation can be reused from one step to the next one and the cost of such a method is really s-1 evaluations despite the method still has s stages. This behaviour is true only for successful steps, if the step is rejected after the error estimation phase, no evaluation is saved. For an fsal method, we have cs = 1 and asi = bi for all i.

See Also:

EulerIntegrator, ClassicalRungeKuttaIntegrator, GillIntegrator, MidpointIntegrator

Field Summary

protected SwitchingFunctionsHandler

switchesHandler Switching functions handler.

Constructor Summary

protected

RungeKuttaIntegrator(boolean fsal, double[] c, double[][] a, double[] b, org.jscience.mathematics.analysis.ode.RungeKuttaStepInterpolator prototype, double step) Simple constructor.

Method Summary

void	addSwitchingFunction(SwitchingFunction function, double maxCheckInterval, double convergence) Add a switching function to the integrator.
abstract java.lang.String	getName() Get the name of the method.
StepHandler	getStepHandler() Get the step handler for this integrator.
void	integrate(FirstOrderDifferentialEquations equations, double t0, double[] y0, double t, double[] y) Integrate the differential equations up to the given time
void	setStepHandler(StepHandler handler) Set the step handler for this integrator.

Methods inherited from class java.lang.Object

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

Field Detail

switchesHandler

protected SwitchingFunctionsHandler switchesHandler

Switching functions handler.

Constructor Detail

RungeKuttaIntegrator

protected RungeKuttaIntegrator(boolean fsal,
                               double[] c,
                               double[][] a,
                               double[] b,
                               org.jscience.mathematics.analysis.ode.RungeKuttaStepInterpolator prototype,
                               double step)

Simple constructor. Build a Runge-Kutta integrator with the given step. The default step handler does nothing.

Parameters:

fsal - indicate that the method is an fsal

c - time steps from Butcher array (without the first zero)

a - internal weights from Butcher array (without the first empty row)

b - external weights for the high order method from Butcher array

prototype - prototype of the step interpolator to use

step - integration step

Method Detail

getName

public abstract java.lang.String getName()

Get the name of the method.

Specified by:

getName in interface FirstOrderIntegrator

Specified by:

getName in interface Named

Returns:

name of the method

setStepHandler

public void setStepHandler(StepHandler handler)

Set the step handler for this integrator. The handler will be called by the integrator for each accepted step.

Specified by:

setStepHandler in interface FirstOrderIntegrator

Parameters:

handler - handler for the accepted steps

getStepHandler

public StepHandler getStepHandler()

Get the step handler for this integrator.

Specified by:

getStepHandler in interface FirstOrderIntegrator

Returns:

the step handler for this integrator

addSwitchingFunction

public void addSwitchingFunction(SwitchingFunction function,
                                 double maxCheckInterval,
                                 double convergence)

Add a switching function to the integrator.

Specified by:

addSwitchingFunction in interface FirstOrderIntegrator

Parameters:

function - switching function

maxCheckInterval - maximal time interval between switching function checks (this interval prevents missing sign changes in case the integration steps becomes very large)

convergence - convergence threshold in the event time search

integrate

public void integrate(FirstOrderDifferentialEquations equations,
                      double t0,
                      double[] y0,
                      double t,
                      double[] y)
               throws DerivativeException,
                      IntegrationException

Description copied from interface: FirstOrderIntegrator

Integrate the differential equations up to the given time

Specified by:

integrate in interface FirstOrderIntegrator

Parameters:

equations - differential equations to integrate

t0 - initial time

y0 - initial value of the state vector at t0

t - target time for the integration (can be set to a value smaller thant t0 for backward integration)

y - placeholder where to put the state vector at each successful step (and hence at the end of integration), can be the same object as y0

Throws:

DerivativeException - this exception is propagated to the caller if the underlying user function triggers one

IntegrationException - if the integrator cannot perform integration