Ordinary Differential Equation Solvers

ODE_MOSHIER is a C library which solves systems of ordinary differential equations. Two main methods are implemented, the Adams-Bashforth-Moulton integrator, and the Runge-Kutta integrator, by Steven Moshier.


ODE_MOSHIER is available in a C version.

Related Data and Programs:

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

NMS, a FORTRAN90 library which includes a wide variety of numerical software.

ODE, a C library which solves a system of ordinary differential equations, by Shampine and Gordon.

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 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 Watt and Shampine RKF45 ODE solver.

TEST_ODE, a FORTRAN90 library which contains routines which define some test problems for ODE solvers.


Steven Moshier


  1. Benku Thomas,
    The Runge-Kutta Methods,
    Volume 11, Number 4, April 1986, pages 191-192.
  2. 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:

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

Last revised on 16 January 2012.