rkf45

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

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 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.

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Author:

This Python implementation was written by Peter Monk.

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:

• rf45.py, the source code;
• rf45.sh, runs all the tests.
• rkf45.txt, the output file.

• f_lor.py, a file which defines the Lorenz oscillator.