midpoint


midpoint, a Python code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.

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. This code uses the nonlinear equation solver fsolve().

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

midpoint is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a FreeFem++ version and a MATLAB version and an Octave version and a Python version and an R version.

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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.