midpoint_explicit


midpoint, a C code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also known as the modified Euler method.

Licensing:

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

Languages:

midpoint_explicit 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 and an R version

Related Data and codes:

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

midpoint_explicit_test

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

midpoint_gsl_test, a C code which calls the Gnu Scientific Library (GSL) implicit midpoint method solver for ordinary differential equation (ODE), and uses gnuplot() to plot the resulting solution.

rk4, a C 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 06 April 2021.