On the exact and numerical solutions to the FitzHugh-Nagumo equation

Abstract

In this paper, with the help of a computer package program, the auto-Backlund transformation method (aBTM) and the finite forward difference method are used for obtaining the wave solutions and the numeric and exact approximations to the FitzHugh-Nagumo (F-N) equation, respectively. We successfully obtain some wave solutions to this equation by using aBTM. We then employ the finite difference method (FDM) in approximating the exact and numerical solutions to this equation by taking one of the obtained wave solutions into consideration. We also present the comparison between exact and numeric approximations and support the comparison with a graphic plot. Moreover, the Fourier von-Neumann stability analysis is used in checking the stability of the numeric scheme. We also present the L-2 and L-infinity error norms of the solutions to this equation.