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Summary  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 ; L  2 )‐norm. A wide set of numerical evidences which provide the convergence rate of the new algorithm are presented and critically discussed.

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