RK4
Runge-Kutta 4th Order ODE Solver

RK4 is a Python library which implements a simple Runge-Kutta solver for an initial value problem.

The rk4() function does not include any error estimator. It takes a single step at a time, requiring the user to control the step size.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

RK4 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, creating graphics output using matplotlib.

RKF45, a Python library which implements the Runge-Kutta-Fehlberg ODE solver.

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.

Source Code:

• rk4.py, takes one Runge Kutta step for a scalar or vector ODE.
• rk4.sh, runs all the tests.
• rk4.txt, the output file.

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