“…The finite-difference method (Hildebrand, 1968;Morton and Mayers, 1996;Richtmyer and Morton, 1967) is widely used by the scientific community for the numerical solution of reaction-diffusion equations; however, there are comparatively few studies that give stability and convergence results (see for example Ascher et al, 1995;Beckett and Mackenzie, 2001;Hoff, 1978;Jerome, 1984;Li et al, 1994;Mickens, 2003;Pao, 1998Pao, , 1999Pao, , 2002Pujol and Grimalt, 2002). The need for a rigorous numerical analysis is due to the well-known (but often neglected) fact that the dynamics of the approximations of nonlinear differential equations (DEs) can differ significantly from that of the original DEs themselves.…”