Numerical Schemes for Time-Space Fractional Vibration Equations

doi:10.4208/aamm.OA-2020-0066

	Numerical Schemes for Time-Space Fractional Vibration Equations
	Zhang, Jingna 3; Aleroev, Temirkhan S.2; Tang, Yifa 1,4; Huang, Jianfei 3
刊名	ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
	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
DOI	10.4208/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
出版者	GLOBAL SCIENCE PRESS
WOS记录号	WOS:000640122800004
内容类型	期刊论文
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Moscow State Univ Civil Engn, Yaroslayskoe Shosse 26, Moscow 129337, Russia 3.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, 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.