ODE
Shampine and Gordon ODE Solver

ODE is 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
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

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 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.

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

Author:

Lawrence Shampine, Marilyn Gordon.

Reference:

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

Source Code:

• ode.cpp, the source code.
• ode.hpp, the include file.
• ode.sh, commands to compile the source code.

Examples and Tests:

• ode_prb.cpp, a sample calling program.
• ode_prb.sh, commands to compile and run the sample program.
• ode_prb_output.txt, the output file.

List of Routines:

• DE carries out the ODE solution algorithm.
• I4_SIGN returns the sign of an I4.
• INTRP approximates the solution at XOUT by polynomial interpolation.
• ODE is the user interface to an ordinary differential equation solver.
• R8_ABS returns the absolute value of an R8.
• R8_ADD adds two R8's.
• R8_EPSILON returns the R8 roundoff unit.
• R8_MAX returns the maximum of two R8's.
• R8_MIN returns the minimum of two R8's.
• R8_SIGN returns the sign of an R8.
• STEP integrates the system of ODEs one step, from X to X+H.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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