# backward_euler

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.

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_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.

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### Source Code:

• backward_euler.m, a version of the backward Euler method that solves the backward Euler equation using fsolve() from the MATLAB Optimization toolbox.

Last revised on 11 October 2020.