KMS Of Academy of mathematics and systems sciences, CAS
| Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative | |
Arshad, Sadia1,6; Huang, Jianfei2; Khaliq, Abdul Q. M.3,4; Tang, Yifa1,5
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| 2017-12-01 | |
| Source Publication | JOURNAL OF COMPUTATIONAL PHYSICS
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| ISSN | 0021-9991 |
| Volume | 350Pages:1-15 |
| Abstract | In this paper, a finite difference scheme is proposed to solve time-space fractional diffusion equation which has second-order accuracy in both time and space direction. The time and space fractional derivatives are considered in the senses of Caputo and Riesz, respectively. First, the centered difference approach is used to approximate the Riesz fractional derivative in space. Then, the obtained fractional ordinary differential equations are transformed into equivalent Volterra integral equations. And then, the trapezoidal rule is utilized to approximate the Volterra integral equations. The stability and convergence of our scheme are proved via mathematical induction method. Finally, numerical experiments are performed to confirm the high accuracy and efficiency of our scheme. (C) 2017 Elsevier Inc. All rights reserved. |
| Keyword | Fractional diffusion equation Caputo derivative Riesz derivative Trapezoidal rule |
| DOI | 10.1016/j.jcp.2017.08.038 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11371357] ; National Natural Science Foundation of China[11426141] ; ITER-China[2014GB124005] |
| WOS Research Area | Computer Science ; Physics |
| WOS Subject | Computer Science, Interdisciplinary Applications ; Physics, Mathematical |
| WOS ID | WOS:000413379000001 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/26767 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Arshad, Sadia; Tang, Yifa |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China 3.Middle Tennessee State Univ, Dept Math Sci, Murfreesboro, TN 37132 USA 4.Middle Tennessee State Univ, Ctr Computat Sci, Murfreesboro, TN 37132 USA 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 6.COMSATS Inst Informat Technol, Lahore, Pakistan |
| Recommended Citation GB/T 7714 | Arshad, Sadia,Huang, Jianfei,Khaliq, Abdul Q. M.,et al. Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017,350:1-15. |
| APA | Arshad, Sadia,Huang, Jianfei,Khaliq, Abdul Q. M.,&Tang, Yifa.(2017).Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative.JOURNAL OF COMPUTATIONAL PHYSICS,350,1-15. |
| MLA | Arshad, Sadia,et al."Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative".JOURNAL OF COMPUTATIONAL PHYSICS 350(2017):1-15. |
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