Integrate an initial value problem using 5th order Runge-Kutta method with adaptive stepsize control. More...

#include <vtkRungeKutta45.h>

Inheritance diagram for vtkRungeKutta45:

Collaboration diagram for vtkRungeKutta45:

Public Types
typedef vtkInitialValueProblemSolver	Superclass
Public Member Functions
virtual int	IsA (const char *type)
vtkRungeKutta45 *	NewInstance () const
void	PrintSelf (ostream &os, vtkIndent indent)

virtual int	ComputeNextStep (double xprev, double xnext, double t, double &delT, double maxError, double &error)
virtual int	ComputeNextStep (double xprev, double dxprev, double *xnext, double t, double &delT, double maxError, double &error)
virtual int	ComputeNextStep (double xprev, double xnext, double t, double &delT, double &delTActual, double minStep, double maxStep, double maxError, double &error)
virtual int	ComputeNextStep (double xprev, double dxprev, double *xnext, double t, double &delT, double &delTActual, double minStep, double maxStep, double maxError, double &error)
Static Public Member Functions
static int	IsTypeOf (const char *type)
static vtkRungeKutta45 *	SafeDownCast (vtkObjectBase *o)
static vtkRungeKutta45 *	New ()
Protected Member Functions
virtual vtkObjectBase *	NewInstanceInternal () const
	vtkRungeKutta45 ()
	~vtkRungeKutta45 ()
virtual void	Initialize ()
int	ComputeAStep (double xprev, double dxprev, double *xnext, double t, double &delT, double &error)
Protected Attributes
double *	NextDerivs [6]
Static Protected Attributes
static double	A [5]
static double	B [5][5]
static double	C [6]
static double	DC [6]

Detailed Description

Integrate an initial value problem using 5th order Runge-Kutta method with adaptive stepsize control.

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

See also:: vtkInitialValueProblemSolver vtkRungeKutta4 vtkRungeKutta2 vtkFunctionSet

Tests:: vtkRungeKutta45 (Tests)

Definition at line 43 of file vtkRungeKutta45.h.

Member Typedef Documentation

typedef vtkInitialValueProblemSolver vtkRungeKutta45::Superclass

Reimplemented from vtkInitialValueProblemSolver.

Definition at line 46 of file vtkRungeKutta45.h.

Constructor & Destructor Documentation

vtkRungeKutta45::vtkRungeKutta45 ( ) [protected]

vtkRungeKutta45::~vtkRungeKutta45 ( ) [protected]

Member Function Documentation

static int vtkRungeKutta45::IsTypeOf ( const char * name ) [static]

Return 1 if this class type is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkInitialValueProblemSolver.

virtual int vtkRungeKutta45::IsA ( const char * name ) [virtual]

Return 1 if this class is the same type of (or a subclass of) the named class. Returns 0 otherwise. This method works in combination with vtkTypeMacro found in vtkSetGet.h.

Reimplemented from vtkInitialValueProblemSolver.

static vtkRungeKutta45* vtkRungeKutta45::SafeDownCast ( vtkObjectBase * o ) [static]

Reimplemented from vtkInitialValueProblemSolver.

virtual vtkObjectBase* vtkRungeKutta45::NewInstanceInternal ( ) const [protected, virtual]

Reimplemented from vtkInitialValueProblemSolver.

vtkRungeKutta45* vtkRungeKutta45::NewInstance ( ) const

Reimplemented from vtkInitialValueProblemSolver.

void vtkRungeKutta45::PrintSelf	(	ostream &	os,
		vtkIndent	indent
	)		`[virtual]`

Methods invoked by print to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from vtkInitialValueProblemSolver.

static vtkRungeKutta45* vtkRungeKutta45::New ( ) [static]

Construct a vtkRungeKutta45 with no initial FunctionSet.

Reimplemented from vtkObject.

virtual int vtkRungeKutta45::ComputeNextStep	(	double *	xprev,
		double *	xnext,
		double	t,
		double &	delT,
		double	maxError,
		double &	error
	)		`[inline, virtual]`

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

Reimplemented from vtkInitialValueProblemSolver.

Definition at line 68 of file vtkRungeKutta45.h.

virtual int vtkRungeKutta45::ComputeNextStep	(	double *	xprev,
		double *	dxprev,
		double *	xnext,
		double	t,
		double &	delT,
		double	maxError,
		double &	error
	)		`[inline, virtual]`

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

Reimplemented from vtkInitialValueProblemSolver.

Definition at line 77 of file vtkRungeKutta45.h.

virtual int vtkRungeKutta45::ComputeNextStep	(	double *	xprev,
		double *	xnext,
		double	t,
		double &	delT,
		double &	delTActual,
		double	minStep,
		double	maxStep,
		double	maxError,
		double &	error
	)		`[inline, virtual]`

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

Reimplemented from vtkInitialValueProblemSolver.

Definition at line 87 of file vtkRungeKutta45.h.

virtual int vtkRungeKutta45::ComputeNextStep	(	double *	xprev,
		double *	dxprev,
		double *	xnext,
		double	t,
		double &	delT,
		double &	delTActual,
		double	minStep,
		double	maxStep,
		double	maxError,
		double &	error
	)		`[virtual]`

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

Implements vtkInitialValueProblemSolver.

virtual void vtkRungeKutta45::Initialize ( ) [protected, virtual]

Reimplemented from vtkInitialValueProblemSolver.