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

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

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In this paper,we give improved error estimates for linearized and nonlinear Crank-Nicolson 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 L2 and H1 norm.However,it is not applicable for the nonlinear scheme.Thus,based on a'cut-off'function and energy analysis method,we get unconditional L2 and H1 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.

complex Ginzburg-Landau equationfinite difference methodunconditional con-vergenceoptimal estimatespointwise error estimates

Yue CHENG、Dongsheng TANG

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School of Mathematics and Statistics,Nantong University,Jiangsu 226019,P.R.China

Jiangsu Xinhai Senior High School,Jiangsu 222005,P.R.China

National Natural Science Foundation of ChinaResearch Start-Up Foundation of Nantong University

11571181135423602051

2024

10.3770/j.issn:2095-2651.2024.02.011

数学研究及应用
大连理工大学

数学研究及应用

影响因子：0.094
ISSN：2095-2651
年,卷(期)：2024.44(2)
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