A Time-Split MacCormack Scheme for Two-Dimensional Nonlinear Reaction-Diffusion Equations
This is an incremental improvement for computational scientists solving nonlinear reaction-diffusion equations, offering a stable explicit scheme with reduced computational cost.
The authors propose a three-level explicit time-split MacCormack scheme for 2D nonlinear reaction-diffusion equations, proving stability and convergence under CFL conditions, and demonstrating convergence rates through numerical experiments.
A three-level explicit time-split MacCormack scheme 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 $L^{\infty}(0,T;L^{2})$-norm. A wide set of numerical evidences which provide the convergence rate of the new algorithm are presented and critically discussed.