RKF45
Runge-Kutta-Fehlberg ODE Solver

RKF45 is a MATLAB 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 described and 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:

DFIELD8, a MATLAB program which interactively displays the direction field of a differential equation, by John Polking.

ODE_PREDATOR_PREY, a MATLAB program which solves a time-dependent predator-prey system using MATLAB's ODE23 solver.

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

PPLANE8, a MATLAB program which interactively displays the phase plane of a differential equation, by John Polking.

TEST_ODE, a MATLAB library which defines some sample ODE's for testing initial value problem 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:

• r8_fehl.m takes one Fehlberg fourth-fifth order step (double precision).
• r8_rkf45.m carries out the Runge-Kutta-Fehlberg method (double precision).
• timestamp.m prints the current YMDHMS date as a time stamp.

Examples and Tests:

• rkf45_test.m, calls all the tests;
• rkf45_test_output.txt, the output file;
• rkf45_test04.m, solves a scalar ODE.
• rkf45_test05.m, solves a vector ODE.
• rkf45_test06.m, solves a scalar ODE, using one-step integration.
• r8_f1.m, evaluates the derivative for the ODE.
• r8_f2.m, evaluates the derivative for the ODE.
• r8_y1x.m, evaluates the exact solution of the ODE.

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