An alternating direction implicit (ADI) difference method is adopted to solve the two-dimensional time-fractional diffusion equation with Dirichlet boundary condition whose solution has some weak singularity at initial time. L1 scheme on uniform mesh is used to discretize the temporal Caputo fractional derivative. Pointwise-in-time error estimate is given for the fully discrete ADI scheme, where the error bound does not blowup when α (the order of fractional derivative) approaches $1^{-}$. It is shown both in theoretically and numerically that the temporal convergence order of the ADI scheme is $O({\tau }^{2\alpha }+\tau t_n^{\alpha -1})$ at time $t=t_n$; hence the scheme is globally $O({\tau }^{\alpha })$ accurate in temporal direction, but it is $O({\tau }^{\min \{2\alpha ,1\}})$ when t is away from 0.

采用交替方向隐式(ADI)差分法求解具有Dirichlet边界条件的二维时间分数扩散方程，其解在初始时具有弱奇异性。均匀网格上的 L1 方案用于离散时间 Caputo 分数阶导数。为完全离散的 ADI 方案给出了时间点误差估计，其中当α（分数阶导数）接近时，误差界限不会扩大$1^{-}$. 从理论上和数值上都表明，ADI 方案的时间收敛顺序为$哦({\tau }^{2\alpha }+\tau {吨}_n^{\alpha -1})$ 时 $吨={吨}_n$; 因此该计划是全球性的$哦({\tau }^{\alpha })$ 在时间方向上准确，但它是 $哦({\tau }^{\mathrm{分钟}\{2\alpha ,1\}})$当t远离 0 时。