But anything which uses matrices (aka. systems of linear differential equations), always runs into some pathological cases. Quite often, they aren't even uncommon.
Systems which have vastly different time constants in the same system are ALWAYS a problem. Simulating RF circuits or phase locked loops is always an issue.
Computational fluid dynamics always has boundary conditions that challenge infinity/zero and drive the solver crazy.
Something as pedestrian as simulating basic cotton cloth accurately is problematic (the warp/weft redistributes energy on a much faster time scale than gravity pulls the cloth down).
A lot of people did a lot of research and put in a lot of programming hours to make solving these problems relatively easy without understanding the gory details.