**backward_euler_fixed**,
a MATLAB code which
solves one or more ordinary differential equations (ODE)
using the (implicit) backward Euler method, using fixed point iteration
to solve the implicit equation.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

**backward_euler_fixed** is available in
a MATLAB version and
an Octave version and
a Python version.

backward_euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) backward Euler method, using fsolve() to solve the implicit equation.

cauchy_method, a MATLAB code which solves one or more ordinary differential equations (ODE) using the Cauchy method.

euler, a MATLAB code which solves one or more ordinary differential equations (ODE) using the forward Euler method.

leapfrog, a MATLAB code which uses the leapfrog method to solve a second order ordinary differential equation (ODE) of the form y''=f(t,y).

midpoint, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method.

midpoint_explicit, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (explicit) midpoint method, also called the modified Euler method.

midpoint_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) midpoint method, using a simple fixed-point iteration to solve the implicit equation.

rk12, a MATLAB code which implements Runge-Kutta solvers of orders 1 and 2 for a system of ordinary differential equations (ODE).

rk23, a MATLAB code which implements Runge-Kutta ODE solvers of orders 2 and 3.

rk34, a MATLAB code which implements Runge-Kutta ODE solvers of orders 3 and 4.

rk4, a MATLAB code which applies the fourth order Runge-Kutta (RK) algorithm to estimate the solution of an ordinary differential equation (ODE).

rk45, a MATLAB code which implements Runge-Kutta ODE solvers of orders 4 and 5.

rkf45, a MATLAB code which implements the Runge-Kutta-Fehlberg ODE solver.

theta_method, a MATLAB code which solves one or more ordinary differential equations (ODE) using the theta method.

trapezoidal, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method.

trapezoidal_explicit, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (explicit) trapezoidal method.

trapezoidal_fixed, a MATLAB code which solves one or more ordinary differential equations (ODE) using the (implicit) trapezoidal method, using the fixed point method to handle the implicit system.

velocity_verlet, a MATLAB code which uses a version of the velocity Verlet method to solve a secord order ordinary differential equation (ODE) of the form y''=f(t,y).

- backward_euler_fixed.m, a version of the backward Euler method that solves the backward Euler equation using a fixed point iteration.