midpoint_fixed, a C code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, applying a fixed point iteration to solve the associated 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.
The computer code and data files described and made available on this web page are distributed under the MIT license
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 version.
euler, a C code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
midpoint_explicit, a C code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.
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).