@article{Hou2025, 
author = {Chang Hou and Hu Chen},
title = {Stability and pointwise-in-time convergence analysis of a finite difference scheme for a 2D nonlinear multi-term subdiffusion equation},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {3},
pages = {1476-1489},
keywords = {multi-term time fractional, nonlinear subdiffusion, L1 scheme, pointwise-in-time error estimate},
url = {https://www.sciopen.com/article/10.3934/era.2025069},
doi = {10.3934/era.2025069},
abstract = {In this paper, we aim to study the stability and convergence of a finite difference scheme for solving the two-dimensional nonlinear multi-term time fractional subdiffusion equation with weakly singular solutions. We apply the L1 scheme to discretize the multi-term temporal Caputo derivatives, a standard central difference method in space, and a backward formula to approximate the nonlinear term on the uniform mesh, respectively. Stability and pointwise-in-time error estimates are obtained for the fully discrete scheme. The global convergence order is        α    1  , and the local convergence order is 1 in the temporal direction. The theoretical analysis is verified by some numerical results.}
}