RKF45method Class Reference

RKF45method is a class for creating approximate solutions of systems of autonomous ordinary differential equations using an implementation of the Runge-Kutta Fehlberg method of order 4 and 5. More...

List of all members.

Public Member Functions
	RKF45method ()
void	setErrorTolerance (double tol)
	Sets the relative and absolute error tolerance of the solution value after one step of size dt.
double	getErrorTolerance () const
	Returns the current error tolerance.
int	getErrorCode () const
	Returns the error code associated with the RK 45 procedure.
int	advance (DoubleVector &yk, double dt, VectorFunction *fPtr)
	The value of yk is updated with the solution of the ODE starting from yk and advancing one timestep dt.
Protected Attributes
double	errorTolerance
int	errorCode

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Detailed Description

RKF45method is a class for creating approximate solutions of systems of autonomous ordinary differential equations using an implementation of the Runge-Kutta Fehlberg method of order 4 and 5.

The solution procedure is a Runge-Kutta Fehlberg method whose mplementation is provided by the routine rkf45 written by H.A. Watts and L.F. Shampine at Sandia Laboratories, Albuquerque, New Mexico.

The version used is an f2c translation of the fortran routine obtained from www.netlib.org. This translated version has been appended with the f2c support routines required for compilation (so that the complete f2c support libraries need not be included).

Author:

Chris Anderson

Version:

01/22/09

Definition at line 37 of file RKF45method.h.

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Member Function Documentation

int RKF45method::advance	(	DoubleVector &	yk,
		double	dt,
		VectorFunction *	Fptr
	)

The value of yk is updated with the solution of the ODE starting from yk and advancing one timestep dt.

• yk : DoubleVector containing solution at time t = tk
• dt : Timestep
• Fptr : Pointer to to a class that extends the VectorFuntion class

  Returns:

  yk is updated with the solution value at t = tk + dt. The return value is 0 if advance is successful; otherwise the return value is the error code iflag from the rkf45 method. The value of iflag can also be obtained using the getErrorCode() member function. The following description is taken from the rkf45.f source code file.

       iflag = 3 -- integration was not completed because relative error
                    tolerance was too small. relerr has been increased
                    appropriately for continuing.
             = 4 -- integration was not completed because more than
                    3000 derivative evaluations were needed. this
                    is approximately 500 steps.
             = 5 -- integration was not completed because solution
                    vanished making a pure relative error test
                    impossible. must use non-zero abserr to continue.
                    using the one-step integration mode for one step
                    is a good way to proceed.
             = 6 -- integration was not completed because requested
                    accuracy could not be achieved using smallest
                    allowable stepsize. user must increase the error
                    tolerance before continued integration can be
                   attempted.
             = 7 -- it is likely that rkf45 is inefficient for solving
                    this problem. too much output is restricting the
                    natural stepsize choice. use the one-step integrator
                    mode.
             = 8 -- invalid input parameters
                    this indicator occurs if any of the following is
                    satisfied -   neqn .le. 0
                                  t=tout  and  iflag .ne. +1 or -1
                                  relerr or abserr .lt. 0.
                                  iflag .eq. 0  or  .lt. -2  or  .gt. 8

The errorTolerance specified is used to set both the absolute and relative error tolerence values. As dicussed in the comments in original rkf45.f, rkf45Comments.f, the advance() routine should not be used with relative error control smaller than about 1.e-8.

Definition at line 91 of file RKF45method.cpp.

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The documentation for this class was generated from the following files:

• RKF45method.h
• RKF45method.cpp

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