rk2_implicit


rk2_implicit, a Fortran90 code which solves one or more ordinary differential equations (ODE) using a Runge-Kutta order 2 implicit method, with a version of fsolve() handling the associated nonlinear equation, and using a fixed time step. This method is often called the (implicit) midpoint method.

Each 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:

rk2_implicit 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.

Related Data and codes:

rk2_implicit_test

f90_ode, a Fortran90 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:


Last revised on 13 November 2024.