unstable_ode

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.

Licensing:

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

Languages:

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

Author:

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.

Related Data and codes:

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

Source Code:

• 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).