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/*=========================================================================
Program: Visualization Toolkit
Module: vtkRungeKutta45.h
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the above copyright notice for more information.
=========================================================================*/
// .NAME vtkRungeKutta45 - Integrate an initial value problem using 5th
// order Runge-Kutta method with adaptive stepsize control.
// .SECTION Description
// This is a concrete sub-class of vtkInitialValueProblemSolver.
// It uses a 5th order Runge-Kutta method with stepsize control to obtain
// the values of a set of functions at the next time step. The stepsize
// is adjusted by calculating an estimated error using an embedded 4th
// order Runge-Kutta formula:
// Press, W. H. et al., 1992, Numerical Recipes in Fortran, Second
// Edition, Cambridge University Press
// Cash, J.R. and Karp, A.H. 1990, ACM Transactions on Mathematical
// Software, vol 16, pp 201-222
// .SECTION See Also
// vtkInitialValueProblemSolver vtkRungeKutta4 vtkRungeKutta2 vtkFunctionSet
#ifndef __vtkRungeKutta45_h
#define __vtkRungeKutta45_h
#include "vtkInitialValueProblemSolver.h"
class VTK_COMMON_EXPORT vtkRungeKutta45 : public vtkInitialValueProblemSolver
{
public:
vtkTypeMacro(vtkRungeKutta45,vtkInitialValueProblemSolver);
void PrintSelf(ostream& os, vtkIndent indent);
// Description:
// Construct a vtkRungeKutta45 with no initial FunctionSet.
static vtkRungeKutta45 *New();
// Description:
// Given initial values, xprev , initial time, t and a requested time
// interval, delT calculate values of x at t+delTActual (xnext).
// Possibly delTActual != delT. This may occur
// because this solver supports adaptive stepsize control. It tries
// to change to stepsize such that
// the (estimated) error of the integration is less than maxError.
// The solver will not set the stepsize smaller than minStep or
// larger than maxStep (note that maxStep and minStep should both
// be positive, whereas delT can be negative).
// Also note that delT is an in/out argument. vtkRungeKutta45
// will modify delT to reflect the best (estimated) size for the next
// integration step.
// An estimated value for the error is returned (by reference) in error.
// This is the norm of the error vector if there are more than
// one function to be integrated.
// This method returns an error code representing the nature of
// the failure:
// OutOfDomain = 1,
// NotInitialized = 2,
// UnexpectedValue = 3
virtual int ComputeNextStep(double* xprev, double* xnext, double t,
double& delT, double maxError, double& error)
{
double minStep = delT;
double maxStep = delT;
double delTActual;
return this->ComputeNextStep(xprev, 0, xnext, t, delT, delTActual,
minStep, maxStep, maxError, error);
}
virtual int ComputeNextStep(double* xprev, double* dxprev, double* xnext,
double t, double& delT,
double maxError, double& error)
{
double minStep = delT;
double maxStep = delT;
double delTActual;
return this->ComputeNextStep(xprev, dxprev, xnext, t, delT, delTActual,
minStep, maxStep, maxError, error);
}
virtual int ComputeNextStep(double* xprev, double* xnext,
double t, double& delT, double& delTActual,
double minStep, double maxStep,
double maxError, double& error)
{
return this->ComputeNextStep(xprev, 0, xnext, t, delT, delTActual,
minStep, maxStep, maxError, error);
}
virtual int ComputeNextStep(double* xprev, double* dxprev, double* xnext,
double t, double& delT, double& delTActual,
double minStep, double maxStep,
double maxError, double& error);
protected:
vtkRungeKutta45();
~vtkRungeKutta45();
virtual void Initialize();
// Cash-Karp parameters
static double A[5];
static double B[5][5];
static double C[6];
static double DC[6];
double* NextDerivs[6];
int ComputeAStep(double* xprev, double* dxprev, double* xnext, double t,
double& delT, double& error);
private:
vtkRungeKutta45(const vtkRungeKutta45&); // Not implemented.
void operator=(const vtkRungeKutta45&); // Not implemented.
};
#endif
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