rkf45

rkf45, a FORTRAN90 code which implements the Watt and Shampine RKF45 solver for systems of ordinary differential equations (ODEs).

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 computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

rkf45 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

midpoint, a FORTRAN90 code which solves one or more ordinary differential equations (ODE) using the midpoint method.

NMS, a FORTRAN90 code which includes a wide variety of numerical software.

ODE, a FORTRAN90 code which solves a system of ordinary differential equations (ODE), by Shampine and Gordon.

rkf45_test

TEST_ODE, a FORTRAN90 code 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 https://www.netlib.org/ode/ the NETLIB ODE web site.

Source Code:

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