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Numerical Schemes for Time-Space Fractional Vibration Equations

文献类型：期刊论文

作者Zhang, Jingna1; Aleroev, Temirkhan S.2; Tang, Yifa3,4; Huang, Jianfei1
刊名ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
出版日期2021-08-01
卷号13期号:4页码:806-826
关键词Time-space fractional vibration equations ADI scheme stability convergence
ISSN号2070-0733
DOI10.4208/aamm.OA-2020-0066
英文摘要In this paper, we present a numerical scheme and an alternating direction implicit (ADI) scheme for the one-dimensional and two-dimensional time-space fractional vibration equations (FVEs), respectively. Firstly, the considered time-space FVEs are equivalently transformed into their partial integro-differential forms with the classical first order integrals and the Riemann-Liouville derivative. This transformation can weaken the smoothness requirement in time when discretizing the partial integro-differential problems. Secondly, we use the Crank-Nicolson technique combined with the midpoint formula, the weighted and shifted Grunwald difference formula and the second order convolution quadrature formula to deal with the temporal discretizations. Meanwhile, the classical central difference formula and fractional central difference formula are applied to approximate the second order derivative and the Riesz derivative in spatial direction, respectively. Further, an ADI scheme is constructed for the two-dimensional case. Then, the convergence and unconditional stability of the proposed schemes are proved rigorously. Both of the schemes are convergent with the second order accuracy in time and space. Finally, two numerical examples are given to support the theoretical results.
资助项目National Natural Science Foundation of China[11701502] ; National Natural Science Foundation of China[11871065]
WOS研究方向Mathematics ; Mechanics
语种英语
WOS记录号WOS:000640122800004
出版者GLOBAL SCIENCE PRESS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/58508]  
专题中国科学院数学与系统科学研究院
通讯作者Huang, Jianfei
作者单位1.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China
2.Moscow State Univ Civil Engn, Yaroslayskoe Shosse 26, Moscow 129337, Russia
3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式
GB/T 7714		 Zhang, Jingna,Aleroev, Temirkhan S.,Tang, Yifa,et al. Numerical Schemes for Time-Space Fractional Vibration Equations[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS,2021,13(4):806-826.
APA Zhang, Jingna,Aleroev, Temirkhan S.,Tang, Yifa,&Huang, Jianfei.(2021).Numerical Schemes for Time-Space Fractional Vibration Equations.ADVANCES IN APPLIED MATHEMATICS AND MECHANICS,13(4),806-826.
MLA Zhang, Jingna,et al."Numerical Schemes for Time-Space Fractional Vibration Equations".ADVANCES IN APPLIED MATHEMATICS AND MECHANICS 13.4(2021):806-826.

入库方式： OAI收割

来源：数学与系统科学研究院

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