Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

08-010 Gabriel J. Lord, Vera Thümmler.
Freezing stochastic travelling waves

We consider in this paper a new method for computing stochastic travelling waves that freezes the wave in the computational domain so it does not move. We obtain a stochastic partial differential algebraic equation that we then discretize and solve. We compare this to a standard approach of simply solving a stochastic partial differential equation directly and examine wave profiles and wave speeds for the Nagumo equation. We examine the effect of multiplicative and additive noise on the speed of propagation with the noise intensity. For multiplicative Itô noise the wave speed is not always strictly increasing with noise intensity. We illustrate that the method can be applied when nucleation of new stochastic travelling waves occurs with additive noise. Finally we compute using a weaker notion of wave speed to freeze the travelling wave.