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Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions (2002.04467v2)
Published 11 Feb 2020 in math.NA and cs.NA
Abstract: 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.