The Grunwald-Letnikov method for fractional differential equations

doi:10.1016/j.camwa.2011.03.054

	The Grunwald-Letnikov method for fractional differential equations
	Scherer, Rudolf 1; Kalla, Shyam L.2; Tang, Yifa3 ; Huang, Jianfei 3
	2011-08-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	62 期号:3 页码:902-917
摘要	This paper is devoted to the numerical treatment of fractional differential equations. Based on the Grunwald-Letnikov definition of fractional derivatives, finite difference schemes for the approximation of the solution are discussed. The main properties of these explicit and implicit methods concerning the stability, the convergence and the error behavior are studied related to linear test equations. The asymptotic stability and the absolute stability of these methods are proved. Error representations and estimates for the truncation, propagation and global error are derived. Numerical experiments are given. (C) 2011 Elsevier Ltd. All rights reserved.
关键词	Fractional derivatives Fractional differential equations Grunwald-Letnikov approximation Difference methods Binomial coefficients Stability
DOI	10.1016/j.camwa.2011.03.054
语种	英语
资助项目	ITMSFA of the National Science Fund-Ministry of Education, Youth and Science of Bulgaria[02/25/2009] ; State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000294083500008
出版者	PERGAMON-ELSEVIER SCIENCE 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/12486
专题	计算数学与科学工程计算研究所
通讯作者	Scherer, Rudolf
作者单位	1.Karlsruhe Inst Technol, Inst Appl & Numer Math, D-76128 Karlsruhe, Germany 2.Vyas Inst Higher Educ, Inst Math, Jodhpur, Rajasthan, India 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Scherer, Rudolf,Kalla, Shyam L.,Tang, Yifa,et al. The Grunwald-Letnikov method for fractional differential equations[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2011,62(3):902-917.
APA	Scherer, Rudolf,Kalla, Shyam L.,Tang, Yifa,&Huang, Jianfei.(2011).The Grunwald-Letnikov method for fractional differential equations.COMPUTERS & MATHEMATICS WITH APPLICATIONS,62(3),902-917.
MLA	Scherer, Rudolf,et al."The Grunwald-Letnikov method for fractional differential equations".COMPUTERS & MATHEMATICS WITH APPLICATIONS 62.3(2011):902-917.