Runge-Kutta 4th Order ODE Solver

RK4, a C code which implements a simple Runge-Kutta solver for an initial value problem.


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


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:

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

ODE_MOSHIER, a C library which implements the Adams-Bashforth-Moulton and Runge-Kutta (RK) methods of solving systems of ordinary differential equations, by Steven Moshier.


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


  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:

Last revised on 22 April 2020.