2020/02/11 by Joachim Crevat, Crevat, Joachim, Francis Filbet +1
Computer Science · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2002.04467
arxiv created 2020/09/29 · arxiv updated 2020/09/30
This paper is devoted to the numerical approximation of the spatially-extended FitzHugh-Nagumo transport equation with strong local interactions based on a particle method. In this regime, the time step can be subject to stability constraints related to the interaction kernel. To avoid this limitation, our approach is based on higher-order implicit-explicit numerical schemes. Thus, when the magnitude of the interactions becomes large, this method provides a consistent discretization of the macroscopic reaction-diffusion FitzHugh-Nagumo system. We carry out some theoretical proofs and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.