Compact high-order implicit iterative scheme for the two-dimensional time-fractional diffusion equation

In this paper, a compact high-order implicit scheme is presented for the solution of the two-dimensional time-fractional diffusion equation. The Caputo fractional derivative and compact implicit scheme are used for the time and space derivatives respectively. The convergence of the proposed scheme will be shown to be O(τ2−β – h4), where τ, β and h are representing time step, fractional-order and space step respectively. Finally, some numerical examples are provided, which shows the accuracy of the proposed scheme.