@article{Li2023, 
author = {Kexin Li and Hu Chen and Shusen Xie},
title = {Error estimate of L1-ADI scheme for two-dimensional multi-term time fractional diffusion equation},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {4},
pages = {1454-1470},
keywords = {Multi-term fractional derivative, ADI scheme, L1 scheme, finite difference method, time fractional},
url = {https://www.sciopen.com/article/10.3934/nhm.2023064},
doi = {10.3934/nhm.2023064},
abstract = {A two-dimensional multi-term time fractional diffusion equation              D              t                      α              u  (  x  ,  y  ,  t  )  −  Δ  u  (  x  ,  y  ,  t  )  =  f  (  x  ,  y  ,  t  ) is considered in this paper, where              D              t                      α             is the multi-term time Caputo fractional derivative. To solve the equation numerically, L1 discretisation to each fractional derivative is used on a graded temporal mesh, together with a standard finite difference method for the spatial derivatives on a uniform spatial mesh. We provide a rigorous stability and convergence analysis of a fully discrete L1-ADI scheme for solving the multi-term time fractional diffusion problem. Numerical results show that the error estimate is sharp.}
}