RKF45
Runge-Kutta-Fehlberg ODE Solver

RKF45 is a FORTRAN77 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.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

RKF45 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a PYTHON version.

Related Data and Programs:

CWG_ODE, a FORTRAN77 library which implements three ODE solvers by C William Gear.

DRIV, a FORTRAN77 library which solves real or complex systems of ordinary differential equations;

NMS, a FORTRAN77 library which includes the DDRIV package of ODE solvers.

ODE, a FORTRAN77 library which solves a system of ordinary differential equations, by Shampine and Gordon.

ODEPACK, a FORTRAN77 library which contains nine ODE solvers, including LSODE, LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS, by Alan Hindmarsh.

RK4, a FORTRAN77 library which applies the fourth order Runge-Kutta algorithm to estimate the solution of an ordinary differential equation at the next time step.

TEST_ODE, 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.f, the source code;
• rkf45.sh, commands to compile the source code;

Examples and Tests:

• rkf45_prb.f, a sample calling program;
• rkf45_prb.sh, 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.

You can go up one level to the FORTRAN77 source codes.