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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 Publication NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS ISSN 0749-159X Volume 31Issue:6Pages:2080-2109 Abstract 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. Keyword compact difference scheme convergence Kuramoto-Tsuzuki equation Neumann boundary conditions priori estimates DOI 10.1002/num.21979 Language 英语 Funding Project Natural Science Foundation for Colleges and Universities in Jiangsu Province[14KJB110006] ; Jiangsu Province Science Foundation[SBK201220691] WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000364659400015 Publisher WILEY-BLACKWELL Citation statistics Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS] Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/21222 Collection 中国科学院数学与系统科学研究院 Affiliation 1.Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China2.Shandong Univ, Sch Math, Jinan 250100, Peoples R China3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China Recommended CitationGB/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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