org.spaceroots.mantissa.ode

Class RungeKuttaIntegrator

java.lang.Object

org.spaceroots.mantissa.ode.RungeKuttaIntegrator

All Implemented Interfaces:

FirstOrderIntegrator

Direct Known Subclasses:

ClassicalRungeKuttaIntegrator, EulerIntegrator, GillIntegrator, MidpointIntegrator, ThreeEighthesIntegrator

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

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.

Version:

$Id: RungeKuttaIntegrator.java 1719 2007-09-26 19:46:57Z luc $

Author:

L. Maisonobe

See Also:

EulerIntegrator, ClassicalRungeKuttaIntegrator, GillIntegrator, MidpointIntegrator

Field Summary

Fields

Modifier and Type	Field and Description
protected SwitchingFunctionsHandler	switchesHandler Switching functions handler.

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	RungeKuttaIntegrator(boolean fsal, double[] c, double[][] a, double[] b, org.spaceroots.mantissa.ode.RungeKuttaStepInterpolator prototype, double step) Simple constructor.

Method Summary

Modifier and Type	Method and Description
void	addSwitchingFunction(SwitchingFunction function, double maxCheckInterval, double convergence) Add a switching function to the integrator.
double	getCurrentStepsize() Get the current value of the integration stepsize.
double	getCurrentStepStart() Get the current value of the step start time ti.
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.spaceroots.mantissa.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

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,
                      IntegratorException

Description copied from interface: FirstOrderIntegrator

Integrate the differential equations up to the given time.

This method solves an Initial Value Problem (IVP).

Since this method stores some internal state variables made available in its public interface during integration (FirstOrderIntegrator.getCurrentStepsize()), it is not thread-safe.

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 than 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

IntegratorException - if the integrator cannot perform integration

getCurrentStepStart

public double getCurrentStepStart()

Description copied from interface: FirstOrderIntegrator

Get the current value of the step start time t_i.

This method can be called during integration (typically by the object implementing the differential equations problem) if the value of the current step that is attempted is needed.

The result is undefined if the method is called outside of calls to FirstOrderIntegrator.integrate(org.spaceroots.mantissa.ode.FirstOrderDifferentialEquations, double, double[], double, double[])

Specified by:

getCurrentStepStart in interface FirstOrderIntegrator

Returns:

current value of the step start time t_i

getCurrentStepsize

public double getCurrentStepsize()

Description copied from interface: FirstOrderIntegrator

Get the current value of the integration stepsize.

This method can be called during integration (typically by the object implementing the differential equations problem) if the value of the current stepsize that is tried is needed.

The result is undefined if the method is called outside of calls to FirstOrderIntegrator.integrate(org.spaceroots.mantissa.ode.FirstOrderDifferentialEquations, double, double[], double, double[])

Specified by:

getCurrentStepsize in interface FirstOrderIntegrator

Returns:

current value of the stepsize