Shampine and Gordon ODE Solver

ODE is a FORTRAN77 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.


ODE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version..

Related Data and Programs:

CWG_ODE, a FORTRAN77 library which implements three ODE solvers by C William Gear.

DRIV, a FORTRAN77 library which solves real or complex systems of ordinary differential equations;

NMS, a FORTRAN77 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 FORTRAN77 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 FORTRAN77 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 FORTRAN77 source codes.

Last revised on 31 May 2008.