Stability and freezing of waves in non-linear hyperbolic-parabolic systems
Jens Rottmann-Matthes · IMA Journal of Applied Mathematics · 2012
In this note, we consider the application of the freezing method to the approximation of travelling waves, in general hyperbolic–parabolic systems that include the Hodgkin–Huxley model and the FitzHugh–Nagumo equation. The tuple consisting of the profile and the speed of a travelling wave is a stationary solution for the method and we prove its asymptotic stability with optimal rates. Therefore, the method is suitable for the approximation of travelling waves by time integration. Numerical experiments for the FitzHugh–Nagumo equations confirm our results.