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 MIT 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 versionand an R version.

Related Data and codes:

midpoint_fixed_test

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.

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:

• midpoint_fixed.f90, the source code.
• midpoint_fixed.sh, compiles the source code.