Fourth-Order Compact Difference Schemes for 1D Nonlinear Kuramoto-Tsuzuki Equation

doi:10.1002/num.21979

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	Fourth-Order Compact Difference Schemes for 1D Nonlinear Kuramoto-Tsuzuki Equation
	Hu, Xiuling 1; Chen, Shanzhen 2; Chang, Qianshun 1,3
	2015-11-01
发表期刊	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0749-159X
卷号	31 期号:6 页码:2080-2109
摘要	In this article, first, we establish some compact finite difference schemes of fourth-order for 1D nonlinear Kuramoto-Tsuzuki equation with Neumann boundary conditions in two boundary points. Then, we provide numerical analysis for one nonlinear compact scheme by transforming the nonlinear compact scheme into matrix form. And using some novel techniques on the specific matrix emerged in this kind of boundary conditions, we obtain the priori estimates and prove the convergence in L-infinity norm. Next, we analyze the convergence and stability for one of the linearized compact schemes. To obtain the maximum estimate of the numerical solutions of the linearized compact scheme, we use the mathematical induction method. The treatment is that the convergence in L-2 norm is obtained as well as the maximum estimate, further the convergence in L-infinity norm. Finally, numerical experiments demonstrate the theoretical results and show that one of the linearized compact schemes is more accurate, efficient and robust than the others and the previous. It is worthwhile that the compact difference methods presented here can be extended to 2D case. As an example, we present one nonlinear compact scheme for 2D Ginzburg-Landau equation and numerical tests show that the method is accurate and effective. (C) 2015 Wiley Periodicals, Inc.
关键词	compact difference scheme convergence Kuramoto-Tsuzuki equation Neumann boundary conditions priori estimates
DOI	10.1002/num.21979
语种	英语
资助项目	Natural Science Foundation for Colleges and Universities in Jiangsu Province[14KJB110006] ; Jiangsu Province Science Foundation[SBK201220691]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000364659400015
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/21222
专题	中国科学院数学与系统科学研究院
通讯作者	Hu, Xiuling
作者单位	1.Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China 2.Shandong Univ, Sch Math, Jinan 250100, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hu, Xiuling,Chen, Shanzhen,Chang, Qianshun. Fourth-Order Compact Difference Schemes for 1D Nonlinear Kuramoto-Tsuzuki Equation[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2015,31(6):2080-2109.
APA	Hu, Xiuling,Chen, Shanzhen,&Chang, Qianshun.(2015).Fourth-Order Compact Difference Schemes for 1D Nonlinear Kuramoto-Tsuzuki Equation.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,31(6),2080-2109.
MLA	Hu, Xiuling,et al."Fourth-Order Compact Difference Schemes for 1D Nonlinear Kuramoto-Tsuzuki Equation".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 31.6(2015):2080-2109.