rkf45

rkf45, a MATLAB code which implements an RKF45 ODE solver, by Watt and Shampine.

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 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

matlab_ode_solver, a MATLAB 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.

Source Code:

• fehl.m takes one Fehlberg fourth-fifth order step (double precision).
• rkf45.m carries out the Runge-Kutta-Fehlberg method (double precision).