Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative

doi:10.3390/e20050321

	Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative
	Arshad, Sadia 1,2; Baleanu, Dumitru 3,4; Huang, Jianfei 5; Al Qurashi, Maysaa Mohamed 6; Tang, Yifa1,7 ; Zhao, Yue 1,7
	2018-05-01
发表期刊	ENTROPY
ISSN	1099-4300
卷号	20 期号:5 页码:20
摘要	In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grunwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis.
关键词	fractional advection dispersion equation riesz derivative caputo derivative trapezoidal formula
DOI	10.3390/e20050321
语种	英语
资助项目	National Natural Science Foundation of China[11771438] ; National Natural Science Foundation of China[11701502] ; Scientific and Technological Research Council of Turkey (TUBITAK)[TBAG-117F473] ; Higher Education Commission of Pakistan (HEC) under NRPU ; "Research Center of the Center for Female Scientific and Medical Colleges", Deanship of Scientific Research, King Saud University
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000435193100014
出版者	MDPI
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30527
专题	计算数学与科学工程计算研究所
通讯作者	Arshad, Sadia; Tang, Yifa
作者单位	1.Chinese Acad Sci, State Key Lab Sci & Engn Comp LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.COMSATS Inst Informat Technol, Lahore 54500, Pakistan 3.Cankaya Univ, Dept Math, TR-06530 Ankara, Turkey 4.Inst Space Sci, Magurele 077125, Romania 5.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China 6.King Saud Univ, Dept Math, POB 22452, Riyadh 11495, Saudi Arabia 7.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Arshad, Sadia,Baleanu, Dumitru,Huang, Jianfei,et al. Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative[J]. ENTROPY,2018,20(5):20.
APA	Arshad, Sadia,Baleanu, Dumitru,Huang, Jianfei,Al Qurashi, Maysaa Mohamed,Tang, Yifa,&Zhao, Yue.(2018).Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative.ENTROPY,20(5),20.
MLA	Arshad, Sadia,et al."Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative".ENTROPY 20.5(2018):20.