A novel three-level time-split approach for solving two-dimensional nonlinear unsteady convection-diffusion-reaction equation

This paper considers a deep analysis of three-level explicit time-split MacCormack method, namely the locally one-dimensional for numerical solution two-dimensional nonlinear evolutionary advection-diffusion equation subjects to suitable initial and boundary conditions. The splitting reduces computational cost algorithm. Under time-step restriction, both theoretical results on stability error estimates scheme are deeply analyzed in \(L^{m}(0,T;L^{2})\)-norm (\(m=1,2,\infty\)). experiments suggest that proposed algorithm is easy implement, temporal second-order convergent fourth-order accurate space. shows utility efficiency considered method.