Runge-Kutta-Fehlberg ODE Solver

RKF45, a C++ code which implements the Watt and Shampine RKF45 ODE solver.

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.


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


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:

ODE, a C++ library which solves a system of ordinary differential equations, by Shampine and Gordon.

RK4, a C++ library which applies the fourth order Runge-Kutta algorithm to estimate the solution of an ordinary differential equation at the next time step.



  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:

Last revised on 07 April 2020.