RKF45
Runge-Kutta-Fehlberg ODE Solver

RKF45 is a FORTRAN90 library which implements the Watt and Shampine RKF45 ODE solver.

The RKF45 ODE solver is a Runge-Kutta-Fehlberg algorithm for solving an ordinary differential equation, with automatic error estimation using rules of order 4 and 5.

Related Data and Programs:

CWG_ODE is a FORTRAN77 library which contains three ODE solvers by C William Gear.

LSODI is a FORTRAN77 library which implements the Livermore Solver for Ordinary Differential Equations, Implicit case.

NMS is a FORTRAN90 library which includes a wide variety of numerical software.

ODE is a FORTRAN90 library which contain the Shampine and Allen ODE solver.

POLKING is a pair of MATLAB routines, DFIELD and PPLANE, for solving and displaying the solution of differential equations and their phase planes.

RKF45 is also available in a C++ version. and a FORTRAN77 version.

TEST_ODE is a FORTRAN90 library which contains routines which define some test problems for ODE solvers.

Reference:

1. Erwin Fehlberg,
   Low-order Classical Runge-Kutta Formulas with Stepsize Control,
   NASA Technical Report R-315, 1969.
2. Lawrence Shampine, Herman Watts, S Davenport,
   Solving Non-stiff Ordinary Differential Equations - The State of the Art,
   SIAM Review,
   Volume 18, pages 376-411, 1976.
3. The source code for Shampine and Watt's original FORTRAN77 routine is available at http://www.netlib.org/ode/ the NETLIB ODE web site.

Source Code:

• rkf45.f90, the source code;
• rkf45.csh, commands to compile the source code;

Examples and Tests:

• rkf45_prb.f90, a sample calling program;
• rkf45_prb.csh, commands to compile and run the sample calling program;
• rkf45_prb_output.txt, the output file;

List of Routines:

• R4_FEHL takes one Fehlberg fourth-fifth order step (single precision).
• R4_RKF45 carries out the Runge-Kutta-Fehlberg method (single precision).
• R8_FEHL takes one Fehlberg fourth-fifth order step (double precision).
• R8_RKF45 carries out the Runge-Kutta-Fehlberg method (double precision).
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.

You can go up one level to the FORTRAN90 source codes.