Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative

doi:10.1016/j.jcp.2017.08.038

	Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative
	Arshad, Sadia 1,6; Huang, Jianfei 2; Khaliq, Abdul Q. M.3,4; Tang, Yifa1,5
	2017-12-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	350 页码:1-15
摘要	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.
关键词	Fractional diffusion equation Caputo derivative Riesz derivative Trapezoidal rule
DOI	10.1016/j.jcp.2017.08.038
语种	英语
资助项目	National Natural Science Foundation of China[11371357] ; National Natural Science Foundation of China[11426141] ; ITER-China[2014GB124005]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000413379000001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26767
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, 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
推荐引用方式 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.