Numerical Integration of ODEs with Forward Euler and Backward Euler in Python and Matlab @Eigensteve

Uploaded December 2022 | Updated September 2026, 2 weeks ago

In this video, we code up the Forward Euler and Backward Euler integration schemes in Python and Matlab, investigating stability and error as a function of the time step. We test these integrators on the simple spring-mass-damper system, where we have an analytic solution to compare against.

Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/

Codes (Python): http://faculty.washington.edu/sbrunton/me564/python/L17_pend.ipynb and http://faculty.washington.edu/sbrunton/me564/python/L17_simpend.ipynb
Codes (Matlab): http://faculty.washington.edu/sbrunton/me564/matlab/L17_pend.m and http://faculty.washington.edu/sbrunton/me564/matlab/L17_simpend.m

@eigensteve on Twitter
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This video was produced at the University of Washington

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0:00 Problem setup
8:39 Matlab code example
20:20 Python code example

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