Analytical and numerical solutions of a two-dimensional multiterm time-fractional diffusion model

In this paper, we consider a two-dimensional multiterm time-fractional diffusion model equation in a rectangular domain. Its analytical solution is obtained by the method of separation of variables. We present an alternating direction implicit (ADI) scheme by using the Legendre spectral method in space and weighted and shifted Grunwald difference operators in time. Stability and convergence of the approximation scheme are established by L-2-norm and L-infinity-norm. Especially, the corrected weighted shifted Grunwald difference (CWSGD) scheme is utilized to improve the convergence accuracy. Numerical examples are given to illustrate the theoretical results. The results indicate that the present numerical method is effective for this general multiterm time-fractional diffusion model.