  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.
