An efficient characteristic finite difference S-DDM scheme for convection–diffusion equations

Abstract

In this paper, an efficient splitting domain decomposition method scheme for solving time-dependent convection–diffusion reaction equations is analyzed. A three-step method along each direction is used to solve the solution over each block-divided sub-domain at every time interval. The new solutions are firstly solved by the quadratic interpolation. Then, the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the new solutions. Lastly, the solutions and fluxes in the interiors of sub-domains are computed by the splitting implicit characteristic difference method. By some auxiliary lemmas and the defined intermediate exact solution, the stability and error estimate are given in discrete L2-norm. We further prove that our scheme is of second-order convergence in space and of first-order convergence in time. Numerical experiments are presented to validate theoretical result.