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Fourth-Order Compact Difference Schemes for 1D Nonlinear Kuramoto-Tsuzuki Equation
Hu, Xiuling1; Chen, Shanzhen2; Chang, Qianshun1,3
2015-11-01
Source PublicationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN0749-159X
Volume31Issue:6Pages:2080-2109
AbstractIn 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.
Keywordcompact difference scheme convergence Kuramoto-Tsuzuki equation Neumann boundary conditions priori estimates
DOI10.1002/num.21979
Language英语
Funding ProjectNatural Science Foundation for Colleges and Universities in Jiangsu Province[14KJB110006] ; Jiangsu Province Science Foundation[SBK201220691]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000364659400015
PublisherWILEY-BLACKWELL
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21222
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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