Shampine and Gordon ODE Solver

ODE, a C library which solves a system of ordinary differential equations, 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 GNU LGPL license.


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

Related Data and Programs:


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.

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.

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


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.