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Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative
Arshad, Sadia1,2; Baleanu, Dumitru3,4; Huang, Jianfei5; Al Qurashi, Maysaa Mohamed6; Tang, Yifa1,7; Zhao, Yue1,7
2018-05-01
Source PublicationENTROPY
ISSN1099-4300
Volume20Issue:5Pages:20
AbstractIn 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.
Keywordfractional advection dispersion equation riesz derivative caputo derivative trapezoidal formula
DOI10.3390/e20050321
Language英语
Funding ProjectNational 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 Research AreaPhysics
WOS SubjectPhysics, Multidisciplinary
WOS IDWOS:000435193100014
PublisherMDPI
Citation statistics
Cited Times:6[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30527
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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