**backward_euler**,
a Python code which
solves one or more ordinary differential equations (ODE)
using the (implicit) backward Euler method, using fsolve()
for 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().

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

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

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- backward_euler.py, the source code.
- backward_euler.sh, runs all the tests.
- backward_euler.txt, the output file.