RKF45
Runge-Kutta-Fehlberg ODE Solver

RKF45 is a Python library which implements the Watt and Shampine RKF45 solver for systems of ordinary differential equations (ODE's).

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 FORTRAN90 version and a MATLAB version and a PYTHON version.

Related Data and Programs:

LORENZ_ODE, a Python program which approximates solutions to the Lorenz system of ordinary differential equations (ODE's) creating graphics output using matplotlib.

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

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

Source Code:

• rf45.py, the source code; the code.

Examples and Tests:

• rkf45_test.py, the sample test code;
• f_lor.py, a file which defines the Lorenz oscillator.

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