Numerical Schemes for Time-Space Fractional Vibration Equations

doi:10.4208/aamm.OA-2020-0066

CSpace

	Numerical Schemes for Time-Space Fractional Vibration Equations
	Zhang, Jingna 1; Aleroev, Temirkhan S.2; Tang, Yifa 3,4; Huang, Jianfei 1
	2021-08-01
发表期刊	ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
ISSN	2070-0733
卷号	13 期号:4 页码:806-826
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.
关键词	Time-space fractional vibration equations ADI scheme stability convergence
DOI	10.4208/aamm.OA-2020-0066
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied ; Mechanics
WOS记录号	WOS:000640122800004
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58509
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.