trapezoidal, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, with a version of fsolve() handling the associated nonlinear equation, and using a fixed time step.
Each step requires the solution of an implicit nonlinear equation. A corresponding function has been devised, called fsolve_tr(), which carries out the iterative solution process.
The computer code and data files described and made available on this web page are distributed under the MIT license.
trapezoidal is available in a C version and a C++ 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.
backward_euler, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using a version of fsolve() for the implicit equation.
euler, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
fsolve, a Fortran90 code which solves systems of nonlinear equations, inspired by the fsolve() function in minpack(), with special interfaces fsolve_bdf2(), fsolve_be() and fsolve_tr() for handling systems associated with implicit ODE solvers of type bdf2, backward Euler, midpoint, or trapezoidal.
midpoint, a Fortran90 code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.
rk4, a Fortran90 code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).
rkf45, a Fortran90 code which implements the Runge-Kutta-Fehlberg ODE solver.