Finite difference method for time-space linear and nonlinear fractional diffusion equations

doi:10.1080/00207160.2017.1344231

	Finite difference method for time-space linear and nonlinear fractional diffusion equations
	Arshad, Sadia 1,2; Bu, Weiping 3; Huang, Jianfei 4; Tang, Yifa1,5 ; Zhao, Yue 1
	2018
发表期刊	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN	0020-7160
卷号	95 期号:1 页码:202-217
摘要	In this paper a finite difference method is presented to solve time-space linear and nonlinear fractional diffusion equations. Specifically, the centred difference scheme is used to approximate the Riesz fractional derivative in space. A trapezoidal formula is used to solve a system of Volterra integral equations transformed from spatial discretization. Stability and convergence of the proposed scheme is discussed which shows second-order accuracy both in temporal and spatial directions. Finally, examples are presented to show the accuracy and effectiveness of the schemes.
关键词	Fractional diffusion equation finite difference method stability and convergence analysis trapezoidal formula Riesz derivative Caputo derivative
DOI	10.1080/00207160.2017.1344231
语种	英语
资助项目	State Key Program of National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[11371357] ; National Natural Science Foundation of China[11472247] ; National Natural Science Foundation of China[11601460] ; ITER-China Program[2014GB124005] ; Research Foundation of Education Commission of Hunan Province of China[16C1540]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000428749300013
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30051
专题	计算数学与科学工程计算研究所
通讯作者	Arshad, Sadia
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.COMSATS Inst Informat Technol, Lahore, Pakistan 3.Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Sch Math & Computat Sci, Xiangtan, Peoples R China 4.Yangzhou Univ, Coll Math Sci, Yangzhou, Jiangsu, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Arshad, Sadia,Bu, Weiping,Huang, Jianfei,et al. Finite difference method for time-space linear and nonlinear fractional diffusion equations[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2018,95(1):202-217.
APA	Arshad, Sadia,Bu, Weiping,Huang, Jianfei,Tang, Yifa,&Zhao, Yue.(2018).Finite difference method for time-space linear and nonlinear fractional diffusion equations.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,95(1),202-217.
MLA	Arshad, Sadia,et al."Finite difference method for time-space linear and nonlinear fractional diffusion equations".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 95.1(2018):202-217.