A variable‐step high‐order scheme for time‐fractional advection‐diffusion equation with mixed derivatives

We consider a high accuracy numerical scheme for solving the two‐dimensional time‐fractional advection‐diffusion equation including mixed derivatives, where the variable‐step Alikhanov formula and a fourth‐order compact approximation are employed to time and space derivatives, respectively. Under mild assumptions on the time step‐sizes, we obtain the unconditional stability and high‐order convergence (second‐order in time and fourth‐order in space) of the proposed scheme by energy method. The theoretical statements are justified by the numerical experiments.