This paper proposes two novel alternating direction implicit (ADI) difference schemes for solving two-dimensional time-fractional sub-diffusion equations, taking into account the weak initial singularity of the solutions. To accurately capture the rapid evolution near the initial time, the Caputo time-fractional derivative is discretized using a transformed L1 method. Furthermore, central and compact finite difference methods are employed in spatial discretization to enhance computational efficiency. By using a discrete Grönwall inequality, the error estimates in H¹ -norm of the two schemes are obtained. Numerical examples are presented to illustrate the effectiveness of the proposed schemes.
Gao et al. (Thu,) studied this question.