Unconditional and Optimal Pointwise Error Estimates of Finite Difference Methods for the Two-Dimensional Complex Ginzburg-Landau Equation  

作　　者：Yue CHENG Dongsheng TANG 

机构地区：[1]School of Mathematics and Statistics,Nantong University,Jiangsu 226019,P.R.China [2]Jiangsu Xinhai Senior High School,Jiangsu 222005,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第2期248-268,共21页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11571181);the Research Start-Up Foundation of Nantong University(Grant No.135423602051).

摘　　要：In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.

关 键 词：complex Ginzburg-Landau equation finite difference method unconditional convergence optimal estimates pointwise error estimates 

分 类 号：O241.82[理学—计算数学]