The characteristic difference DDM for solving the time-fractional order convection-diffusion equations

In this paper, an efficient characteristic difference domain decomposition method for solving the time-fractional order convection-diffusion equations is developed. A three-step method is used to solve the solution over non-overlapping sub-domain at every time interval. The new solutions are first solved by the the quadratic interpolation. Then, the intermediate fluxes on the interfaces of sub-domains are computed by local multi-point weighted average from the above new solutions. Finally, the solutions and fluxes in the interiors of sub-domains are computed by the implicit characteristic difference method, while the time fractional derivative is approximated by L1-format. By combining the operator splitting technique, we further propose an efficient splitting domain decomposition method for solve the two-dimensional problems. By some auxiliary lemmas, the stability and error estimate are given in discrete L-2-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.