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A gallery of numerical failures

Since quite some time I’ve been willing to create a gallery of numerical failures that would collect pictures in which a certain numerical method failed, with an explanation of what happened. I believe that it can be useful to raise awareness of things that can go wrong using a certain method. And fun to watch too! Hopefully, I’ll find time to get around to doing it at some point :)

For the moment, enjoy a possible way in which the Euler method can fail if you just happened to slide with your \(\Delta x\) to another position with a zero derivative!

^{(Somehow, this plot always reminds me of the scene from the movie Toy Story 2 where the game version of Buzz Lightyear jumps over the circular platforms to the music of Also sprach Zarathustra.)}