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A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam
Liu, Jiankang1; Guo, Bao-Zhu2,3,4
2019-12-01
发表期刊SYSTEMS & CONTROL LETTERS
ISSN0167-6911
卷号134页码:10
摘要In this paper, a novel space semi-discretized numerical scheme which is based on finite volume method is proposed for approximation of uniformly exponential decay of Euler-Bernoulli beam system, which turns out to be an alternative of finite-difference scheme from order reduction point of view. The new scheme is constructed on equidistant grid points without using any numerical viscosity terms. The uniformly exponential decay is proved by the Lyapunov function method and the energy multiplier technique. With construction of a new gradient recovery function, the numerical solution is proved to be convergent to the (weak) solution of the original continuous system. Compared with the existing literature, the proposed approach has potentially achieved the following objectives: a) It removes the introduction of the numerical viscosity term to achieve uniform convergence; b) It can deal with any type of boundary conditions without help of the spectral analysis which is limited only for some special boundary conditions; c) the convergence proof is simplified significantly with the similar techniques in dealing with the continuous counterpart. (C) 2019 Elsevier B.V. All rights reserved.
关键词Beam equation Finite volume method Finite difference method Exponential stability Uniform approximation
DOI10.1016/j.sysconle.2019.104518
收录类别SCI
语种英语
资助项目National Natural Science Foundation of China[11901365] ; National Natural Science Foundation of China[61873260] ; Project of Department of Education of Guangdong Province[2017KZDXM087]
WOS研究方向Automation & Control Systems ; Operations Research & Management Science
WOS类目Automation & Control Systems ; Operations Research & Management Science
WOS记录号WOS:000501653800003
出版者ELSEVIER
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/50403
专题中国科学院数学与系统科学研究院
通讯作者Liu, Jiankang
作者单位1.Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China
2.North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China
3.Acad Sinica, Key Lab Syst & Control, Acad Math & Syst Sci, Beijing 100190, Peoples R China
4.Univ Witwatersrand, Sch Comp Sci & Appl Math, ZA-2050 Johannesburg, South Africa
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Liu, Jiankang,Guo, Bao-Zhu. A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam[J]. SYSTEMS & CONTROL LETTERS,2019,134:10.
APA Liu, Jiankang,&Guo, Bao-Zhu.(2019).A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam.SYSTEMS & CONTROL LETTERS,134,10.
MLA Liu, Jiankang,et al."A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam".SYSTEMS & CONTROL LETTERS 134(2019):10.
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