ode, a FORTRAN90 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 GNU LGPL license.


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

Related Data and Programs:

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


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

TEST_ODE, a FORTRAN90 code 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:

Last revised on 02 August 2020.