Comparative study of some numerical methods for FitzHugh-Nagumo equation

Abstract

The FitzHugh-Nagumo equation has various applications in the fields of flame propagation, logistic population growth, neurophysiology, autocatalytic chemical reaction and nuclear theory. In this work, we construct three versions of nonstandard finite difference schemes in order to solve the FitzHugh-Nagumo equation with specified initial and boundary conditions under three different regimes. Properties of the methods such as positivity and boundedness are studied. The performances of the three methods is compared by computing L1, L∞ errors and CPU time at given time, T = 1.0.