rkf45

rkf45, a Fortran90 code which implements the Watt and Shampine RKF45 solver for systems of ordinary differential equations (ODE).

The 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 information on this web page is distributed under the MIT 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 an Octave version and a Python version.

Related Data and Programs:

rkf45_test

f90_ode_solver, a Fortran90 code which solves one or more differential equations (ODE) using a method of a particular order, either explicit or implicit. Some methods require a nonlinear equation solver. Some methods used a fixed stepsize, while others adapt the stepsize based on an error estimate.

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 https://www.netlib.org/ode/ the NETLIB ODE web site.

Source Code:

• rkf45.f90, the source code;
• rkf45.sh, compiles the source code;