ode, a C code which solves a system of ordinary differential equations (ODE), by Shampine and Gordon.

Given a system of ordinary differential equations of the form

        Y' = F(T,Y)
        Y(T0) = Y0
this program produces a sequence of approximate solution values Y(TOUT) at later times TOUT.


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


ode is available in a C version and a C++ version and a FORTRAN90 version..

Related Data and Programs:


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

midpoint_gsl_test, a C code which calls the Gnu Scientific Library (GSL) implicit midpoint method solver for ordinary differential equation (ODE), and uses gnuplot() to plot the resulting solution.

rk4, a C code which applies the fourth order Runge-Kutta algorithm to estimate the solution of an ordinary differential equation (ODE) at the next time step.

RKF45, a C code which implements the Runge-Kutta-Fehlberg solver for ordinary differential equations (ODE).


Original FORTRAN77 version by Lawrence Shampine, Marilyn Gordon. This C version by John Burkardt.


  1. Lawrence Shampine, Marilyn Gordon,
    Computer Solution of Ordinary Differential Equations: The Initial Value Problem,
    Freeman, 1975,
    ISBN: 0716704617,
    LC: QA372.S416.

Source Code:

Last revised on 21 July 2019.