On sinc discretization and banded preconditioning for linear third-order ordinary differential equations

doi:10.1002/nla.738

	On sinc discretization and banded preconditioning for linear third-order ordinary differential equations
	Bai, Zhong-Zhi1 ; Chan, Raymond H.2; Ren, Zhi-Ru 1
	2011-05-01
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN	1070-5325
卷号	18 期号:3 页码:471-497
摘要	Some draining or coating fluid-flow problems and problems concerning the flow of thin films of viscous fluid with a free surface can be described by third-order ordinary differential equations (ODEs). In this paper, we solve the boundary value problems of such equations by sinc discretization and prove that the discrete solutions converge to the true solutions of the ODEs exponentially. The discrete solution is determined by a linear system with the coefficient matrix being a combination of Toeplitz and diagonal matrices. The system can be effectively solved by Krylov subspace iteration methods, such as GMRES, preconditioned by banded matrices. We demonstrate that the eigenvalues of the preconditioned matrix are uniformly bounded within a rectangle on the complex plane independent of the size of the linear system. Numerical examples are given to illustrate the effective performance of our method. Copyright (C) 2010 John Wiley & Sons, Ltd.
关键词	third-order ordinary differential equation sinc-collocation discretization sinc-Galerkin discretization convergence analysis banded preconditioning Krylov subspace methods
DOI	10.1002/nla.738
语种	英语
资助项目	The National Basic Research Program[2005CB321702] ; China Outstanding Young Scientist Foundation[10525102] ; The Hong Kong Research Grants Council[400508] ; CUHK DAG[2060257]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000290162800012
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/13036
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	1.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Bai, Zhong-Zhi,Chan, Raymond H.,Ren, Zhi-Ru. On sinc discretization and banded preconditioning for linear third-order ordinary differential equations[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2011,18(3):471-497.
APA	Bai, Zhong-Zhi,Chan, Raymond H.,&Ren, Zhi-Ru.(2011).On sinc discretization and banded preconditioning for linear third-order ordinary differential equations.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,18(3),471-497.
MLA	Bai, Zhong-Zhi,et al."On sinc discretization and banded preconditioning for linear third-order ordinary differential equations".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 18.3(2011):471-497.