TY - JOUR AU - Ngondiep, E. PY - 2022 TI - A novel three-level time-split approach for solving two-dimensional nonlinear unsteady convection-diffusion-reaction equation JO - Journal of Mathematics and Computer Science SP - 222--248 VL - 26 IS - 3 AB - This paper considers a deep analysis of a three-level explicit time-split MacCormack method, namely the locally one-dimensional explicit MacCormack for the numerical solution of the two-dimensional nonlinear evolutionary advection-diffusion equation subjects to suitable initial and boundary conditions. The splitting reduces the computational cost of the algorithm. Under a suitable time-step restriction, both theoretical and numerical results on the stability and error estimates of the scheme are deeply analyzed in \(L^{m}(0,T;L^{2})\)-norm (\(m=1,2,\infty\)). The numerical experiments suggest that the proposed algorithm is easy to implement, temporal second-order convergent and fourth-order accurate in space. 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