On sinc discretization and banded preconditioning for linear third-order ordinary differential equations
文献类型：期刊论文
| 作者 | Bai, Zhong-Zhi1 ; Chan, Raymond H.2; Ren, Zhi-Ru1
|
| 刊名 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
 |
| 出版日期 | 2011-05-01 |
| 卷号 | 18期号:3页码:471-497 |
| 关键词 | third-order ordinary differential equation sinc-collocation discretization sinc-Galerkin discretization convergence analysis banded preconditioning Krylov subspace methods |
| ISSN号 | 1070-5325 |
| DOI | 10.1002/nla.738 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000290162800012 |
| 出版者 | WILEY-BLACKWELL |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13035]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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