Shampine and Gordon ODE Solver

ODE is a FORTRAN90 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 FORTRAN77 version and a FORTRAN90 version..

Related Data and Programs:

NMS, a FORTRAN90 library which includes the ddriv package of ODE solvers.

ODEPACK, a FORTRAN77 library which contains nine ODE solvers, including LSODE, LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS, by Alan Hindmarsh.

RK4, a FORTRAN90 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 FORTRAN90 library which implements the Runge-Kutta-Fehlberg ODE solver.

TEST_ODE, a FORTRAN90 library which defines test problems for ODE solvers.


Lawrence Shampine, Marilyn Gordon.


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

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 15 March 2005.