Application of the Crank–Nicolson time integrator to viscoelastic wave equations with boundary feedback damping

Author:

Xu Da1

Affiliation:

1. Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, PR China

Abstract

Abstract We study the numerical solutions for a boundary feedback mechanism on torsional vibrations of a homogeneous viscoelastic rod. The problem is discretized by the Crank–Nicolson scheme based on the trapezoidal rule: while the time derivative is approximated by the trapezoidal rule in a two-step way, a convolution quadrature formula, constructed again from the trapezoidal rule, is used to approximate the integral term. Error estimates of the numerical scheme are derived in the $ l^{\infty }_{t}(0,~\infty ;~L^{2}(0,~1)) $ norm. Results from some numerical experiment are presented.

Funder

National Natural Science Foundation of China

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Mathematics,General Mathematics

Reference29 articles.

1. Zur Theorie der Elastischen Nachwirkung;Boltzmann,1876

2. A nonhomogeneous integrodifferential equation in Hilbert space;Carr;SIAM J. Math. Anal.,1979

3. Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain;Chen;J. Math. Pures Appl.,1979

4. A note on the boundary stabilization of the wave equation;Chen;SIAM J. Control Optim.,1981

5. Modeling, stabilization and control of serially connected beams;Chen;SIAM J. Control Optim.,1987

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3