2010/06/02 by Gabriel J. Lord, Lord, G. J., Thuemmler, V.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Pattern Formation and Solitons (nlin.PS) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1006.0428
openalex publication_date 2010/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider in this paper travelling wave solutions to stochastic partial differential equations and corresponding wave speed. As a particular example we consider the Nagumo equation with multiplicative noise which we mainly consider in the Stratonovich sense. A standard approach to determine the position and hence speed of a wave is to compute the evolution of a level set. We compare this approach against an alternative where the wave position is found by minimizing the L2 norm against a fixed profile. This approach can also be used to stop (or freeze) the wave and obtain a stochastic partial differential algebraic equation that we then discretize and solve. Although attractive as it leads to a smaller domain size it can be numerically unstable due to large convection terms. We compare numerically the different approaches for estimating the wave speed. Minimization against a fixed profile works well provided the support of the reference function is not too narrow. We then use these techniques to investigate the effect of both \Ito and Stratonovich noise on the Nagumo equation as correlation length and noise intensity increases.