@article{Cao2025, 
author = {Jianxiong Cao and Yuexin Xing},
title = {Error analysis of a high-order compact ADI scheme for 2D time-fractional convection-diffusion equation with weakly singular solutions},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {8},
pages = {4763-4784},
keywords = {time-fractional convection-diffusion equation, L2-1σ formula, ADI method, stability, convergence},
url = {https://www.sciopen.com/article/10.3934/era.2025214},
doi = {10.3934/era.2025214},
abstract = {In this paper, we propose a high-order numerical method for the 2D time-fractional convection-diffusion equation with weakly singular solutions, where the time Caputo fractional derivative is approximated by using the    L  2-       1    σ   formula on a nonuniform graded mesh, and the space derivatives are discretized by a fourth-order compact finite difference scheme on a uniform mesh. The fully discrete compact ADI scheme is established by adding a high-order term. The stability and the convergence analyses of the scheme are analyzed in        L    2  -norm by using the discrete energy method. It has been proved that the introduced numerical scheme has spatial fourth-order convergence, and temporal optimal    (  1  +  α  )-   t  h order convergence. The numerical results show that the error estimates are sharp.}
}