Construction and analysis of some nonstandard finite difference methods for the FitzHugh-Nagumo equation

In this work, we construct four versions of nonstandard finite difference schemes in order to solve the FitzHugh-Nagumo equation with specified initial and boundary conditions under three different regimes giving rise to three cases. The properties of the methods such as positivity and boundedness are studied. The numerical experiment chosen is quite challenging due to shock-like profiles. The performance of the four methods is compared by computing L-1, L-infinity errors, rate of convergence with respect to time and central processing unit time at given time, T = 0.5. Error estimates have also been studied for the most efficient scheme.