midpoint_fixed

midpoint_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, with a simple fixed-point iteration to solve the implicit equation, using a fixed time step.

Licensing:

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

Languages:

midpoint_fixed 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 versionand an R version.

Related Data and codes:

midpoint_fixed_test

matlab_ode_solver, a MATLAB code which solves one or more differential equations (ODE) using a method of a particular order, either explicit or implicit. Some methods require a nonlinear equation solver. Some methods used a fixed stepsize, while others adapt the stepsize based on an error estimate.

Reference:

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

Source Code:

• midpoint_fixed.m, a version of the midpoint method that solves the implicit backward Euler step equation using a fixed point iteration taking just 10 steps each time.