@article{Fei2022, 
author = {Mingfa Fei and Wenhao Li and Yulian Yi},
title = {Numerical analysis of a fourth-order linearized difference method for nonlinear time-space fractional Ginzburg-Landau equation},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {10},
pages = {3635-3659},
keywords = {Ginzburg-Landau equation, fractional derivative, L2-1σ scheme, difference method, convergence},
url = {https://www.sciopen.com/article/10.3934/era.2022186},
doi = {10.3934/era.2022186},
abstract = {An efficient difference method is constructed for solving one-dimensional nonlinear time-space fractional Ginzburg-Landau equation. The discrete method is developed by adopting the  L2- 1σ scheme to handle Caputo fractional derivative, while a fourth-order difference method is invoked for space discretization. The well-posedness and a priori bound of the numerical solution are rigorously studied, and we prove that the difference scheme is unconditionally convergent in pointwise sense with the rate of  O(τ2+h4), where  τ and  h are the time and space steps respectively. In addition, the proposed method is extended to solve two-dimensional problem, and corresponding theoretical analysis is established. Several numerical tests are also provided to validate our theoretical analysis.}
}