midpoint

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

Each midpoint step requires the solution of an implicit nonlinear equation representing a backward Euler step. A corresponding function has been devised, called fsolve_be(), which carries out the iterative solution process.

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.

Related Data and codes:

midpoint_test

cpp_ode, a C++ 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.cpp, the source code.
• midpoint.sh, compiles the source code.
• midpoint.hpp, the include file.