bdf2


bdf2, a Fortran77 code which solves one or more ordinary differential equations (ODE) using the (implicit) backward difference formula order 2 (BDF2), with a version of fsolve() handling the associated nonlinear equation, and using a fixed time step.

Licensing:

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

Languages:

bdf2 is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and codes:

bdf2_test

backward_euler, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using a version of fsolve() for the implicit equation.

euler, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the forward Euler method.

fsolve, a Fortran90 code which solves systems of nonlinear equations, inspired by the fsolve() function in minpack(), with special interfaces fsolve_bdf2(), fsolve_be() and fsolve_tr() for handling systems associated with implicit ODE solvers of type bdf2, backward Euler, midpoint, or trapezoidal.

midpoint, a Fortran77 code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, with a version of fsolve() handling the associated nonlinear equations, and using a fixed time step.

rk4, a Fortran90 code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).

rkf45, a Fortran90 code which implements the Runge-Kutta-Fehlberg ODE solver.

trapezoidal, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and a version of fsolve() to handle the nonlinear equation.

Reference:

  1. Catalin Trenchea, John Burkardt,
    Refactorization of the midpoint rule,
    Applied Mathematics Letters,
    Volume 107, September 2020.

Source Code:


Last revised on 01 December 2023.