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Article Dans Une Revue BIT Numerical Mathematics Année : 2021

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

Résumé

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.
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Dates et versions

hal-02472925 , version 1 (10-02-2020)
hal-02472925 , version 2 (29-09-2020)

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Joachim Crevat, Francis Filbet. Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions. BIT Numerical Mathematics, 2021, ⟨10.1007/s10543-021-00844-5⟩. ⟨hal-02472925v2⟩
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