Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions

• Published in: arXiv.org
• Main Authors: Crevat, Joachim, Filbet, Francis
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 29.09.2020
• Subjects: Transport equations
• ISSN: 2331-8422

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.