The "sawtooth" problem is assessed for its use as an indicator of stability in GIMP.  The hypothesis is that the discontinuous changes of stress and velocity represent perturbations from a numerical point of view.  Therefore if a method can acceptably solve the sawtooth problem then it can be viewed as stable from a practical point of view.  The practical definition of stability used here is simply: an algorithm returns toward the true solution after it is perturbed.

The results here suggest that the centered-difference and USL2 algorithms are stable, but USF and USF2 are not.  Indeed USF blew up too quickly to make an interesting movie.

Centered-Difference


USL2


USF2