A three-level time-split MacCormack method for two-dimensional nonlinear reaction-diffusion equations

A three-level explicit time-split MacCormack method is proposed for solving the two-dimensional nonlinear reaction-diffusion equations. The computational cost is reduced thank to the splitting and the explicit MacCormack scheme. Under the well-known condition of Courant-Friedrich-Lewy (CFL) for stability of explicit numerical schemes applied to linear parabolic partial differential equations, we prove the stability and convergence of the method in L^∞(0,T;L²)-norm. A wide set of numerical evidences which provide the convergence rate of the new algorithm are presented and critically discussed.