A compact ADI Crank-Nicolson difference scheme for the two-dimensional time fractional subdiffusion equation

In this paper, a compact alternating direction implicit (ADI) Crank-Nicolson difference scheme is proposed and analysed for the solution of two-dimensional time fractional subdiffusion equation. The Riemann-Liouville time fractional derivative is approximated by the weighted and shifted Grunwald difference operator and the spatial derivative is discretized by a fourth-order compact finite difference method. The stability and convergence of the difference scheme are discussed and theoretically proven by using the energy method. Finally, numerical experiments are carried out to show that the numerical results are in good agreement with the theoretical analysis.