Numerical Analysis of equivariant evolution equations
11-079 Jens Rottmann-Matthes.
Stability and Freezing of Waves in Nonlinear
Hyperbolic-Parabolic Systems
In this note we consider the application
of the freezing method to the approximation of traveling waves
in hyperbolic-parabolic systems such as the Hodgkin-Huxley
model and the FitzHugh-Nagumo equation. The tuple consisting of
the profile and the speed of a traveling 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 traveling waves by time integration. Numerical
experiments for the FitzHugh-Nagumo equations confirm our
results.
