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