Difference Methods for Computing the Ginzburg-Landau Equation in Two Dimensions

doi:10.1002/num.20535

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	Difference Methods for Computing the Ginzburg-Landau Equation in Two Dimensions
	Xu, Qiubin 1; Chang, Qianshun 2
	2011-05-01
发表期刊	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0749-159X
卷号	27 期号:3 页码:507-528
摘要	In this article, three difference schemes of the Ginzburg-Landau Equation in two dimensions are presented. In the three schemes, the nonlinear term is discretized such that nonlinear iteration is not needed in computation. The plane wave solution of the equation is studied and the truncation errors of the three schemes are obtained. The three schemes are unconditionally stable. The stability of the two difference schemes is proved by induction method and the time-splitting method is analysized by linearized analysis. The algebraic multigrid method is used to solve the three large linear systems of the schemes. At last, we compute the plane wave solution and some dynamics of the equation. The numerical results demonstrate that our schemes are reliable and efficient. (c) 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 507-528, 2011
关键词	Ginzburg-Landau equation difference scheme time-splitting scheme convergence stability
DOI	10.1002/num.20535
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000288617300002
出版者	WILEY-BLACKWELL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11661
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Qiubin
作者单位	1.Nanjing Audit Univ, Dept Appl Math, Nanjing 211815, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Xu, Qiubin,Chang, Qianshun. Difference Methods for Computing the Ginzburg-Landau Equation in Two Dimensions[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2011,27(3):507-528.
APA	Xu, Qiubin,&Chang, Qianshun.(2011).Difference Methods for Computing the Ginzburg-Landau Equation in Two Dimensions.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,27(3),507-528.
MLA	Xu, Qiubin,et al."Difference Methods for Computing the Ginzburg-Landau Equation in Two Dimensions".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 27.3(2011):507-528.