A comprehensive numerical investigation of a coupled mathematical model of neuronal excitability

Abstract

In this paper, we begin with a biological interpretation of what the subsequent mathematical and numerical analyses of the FitzHugh-Nagumo model entail. The interaction between action potential variable and recovery variable is then revisited through linear stability analysis around the equilibrium and local stability conditions are determined. Analytical results are compared with numerical simulations. The study aims to show an alternative approach regarding Taylor polynomials and constructed finite difference scheme which play a key role in the numerical approach for the problem. The robustness of the schemes is investigated in terms of convergency and stability of the techniques. Moreover, the numerical simulations are shown. Consequently, a comprehensive investigation of the related model is examined.