backward_euler

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

Unless the right hand side of the ODE is linear in the dependent variable, each backward Euler 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().

Licensing:

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

Languages:

backward_euler is available in a FreeFem++ version and a MATLAB version and an Octave version and a Python version and an R version.

Related Data and codes:

backward_euler_test

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

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

rk12, an Octave code which implements Runge-Kutta ODE solvers of orders 1 and 2.

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

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

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

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

rkf45, an Octave code which implements the Runge-Kutta-Fehlberg ODE solver.

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

Source Code:

• backward_euler.m, a version of the backward Euler method that solves the backward Euler equation using the Octave version of fsolve().