Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation

摘要

In this paper, a Crank-Nicolson-type compact ADI scheme is proposed for solving two-dimensional fractional subdiffusion equation. The unique solvability, unconditional stability and convergence of the scheme are proved rigorously. Two error estimates are presented. One is Ο(τ~(min{2-γ/2,2γ})+h_1~4+h_2~4) in standard H~1 norm, where t is the temporal grid size and h_1, h_2 are spatial grid sizes; the other is O(τ~(2γ) + h_1~4 + h_1~4) in H_γ~1 norm, a generalized norm which is associated with the Riemann-Liouville fractional integral operator. Numerical results are presented to support the theoretical analysis.