**unstable_ode**,
a Python code which
sets up and solves an unstable ordinary differential equation (ODE)
which the backward Euler method incorrectly drives to zero.

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

**unstable_ode** is available in
a MATLAB version and
a Python version.

This example, which demonstrates that the "stability" of the backward Euler method can sometimes completely destroy the correct solution, was thought up and implemented by Catalin Trenchea, to make a point.

python_ode, Python codes which sets up various systems of ordinary differential equations (ODE).

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

- unstable_backward_euler_plot.png, Y(t), Y'(t).
- unstable_midpoint_plot.png, Y(t), Y'(t).