midpoint_fixed


midpoint_fixed, a FORTRAN90 code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, applying a fixed point iteration for the nonlinear equation.

Unless the right hand side of the ODE is linear in the dependent variable, each midpoint step requires the solution of an implicit nonlinear equation. Such equations can be approximately solved using methods such as fixed point iteration.

Licensing:

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

Languages:

midpoint_fixed is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and an Octave version and a Python version.

Related Data and codes:

euler, a FORTRAN90 code which solves one or more ordinary differential equations (ODE) using the forward Euler method.

midpoint_explicit, a FORTRAN90 code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.

midpoint_fixed_test

rk4, a FORTRAN90 code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).

Reference:

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

Source Code:


Last revised on 07 April 2021.