trapezoidal, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, and fsolve to handle the implicit system.
Unless the right hand side of the ODE is linear in the dependent variable, each trapezoidal step requires the solution of an implicit nonlinear equation. Such equations can be approximately solved using methods such as fixed point iteration, or an implicit equation solver like fsolve().
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
trapezoidalal is available in a MATLAB version and an Octave version and a Python version and an R version.
backward_euler, an Octave code which solves one or more ordinary differential equations (ODE) using the backward Euler method.
euler, an Octave code code which solves one or more ordinary differential equations (ODE) using the forward Euler method.
midpoint, an Octave code code which solves one or more ordinary differential equations (ODE) using the midpoint method.
rk12, an Octave code code which implements Runge-Kutta solvers of orders 1 and 2 for a system of ordinary differential equations (ODE).
rk23, an Octave code code which implements Runge-Kutta ODE solvers of orders 2 and 3.
rk34, an Octave code code which implements Runge-Kutta ODE solvers of orders 3 and 4.
rk4, an Octave code code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).
rk45, an Octave code code which implements Runge-Kutta ODE solvers of orders 4 and 5.
rkf45, an Octave code code which implements the Runge-Kutta-Fehlberg ODE solver.
trapezoidal_fixed, an Octave code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, using the fixed point method.