A novel three-level time-split approach for solving two-dimensional nonlinear unsteady convection-diffusion-reaction equation
Eric Ngondiep
Abstract
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. This shows the utility and efficiency of the considered method.