Mathematical Modelling and Numerical Simulations in Nerve Conduction

In this paper we are concerned with the numerical solution of the discrete FitzHugh-Nagumo equation. This equation describes the propagation of impulses across a myelinated axon. We analyse the asymptotic behaviour of the solutions of the considered equation and numerical approximations are computed by a new algorithm, based on a finite difference scheme and on the Newton method. The efficiency of the method is discussed and its performance is illustrated by a set of numerical examples.

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