Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients

doi:10.1016/j.cam.2009.09.027

CSpace

	Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients
	Ding, Zhiqing 1; Xiao, Aiguo 1; Li, Min 2
	2010-02-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	233 期号:8 页码:1905-1914
摘要	A class of weighted finite difference methods (WFDMs) for solving a class of initial-boundary value problems of space fractional partial differential equations with variable coefficients is presented. Their stability and convergence properties are considered. It is proven that the WFDMs are unconditionally-stable for 0 <= r <= 1/2, and conditionally-stable for 1/2 < r <= 1, here r is the weighting parameter subjected to 0 <= r <= 1. Some convergence results are given. These methods, problems and results generalize the corresponding methods, problems and results given in [7,13,10]. Some numerical examples are provided to show the effectiveness of the methods with different weighting parameters. (C) 2009 Elsevier B.V. All rights reserved.
关键词	Left-handed fractional derivative Right-handed fractional derivative Shifted Grunwald formula Weighted finite difference methods Stability Convergence
DOI	10.1016/j.cam.2009.09.027
语种	英语
资助项目	NSF of China[10971175] ; NSF of China[10871207] ; Specialized Research Fund for the Doctoral Program of Higher Education of China ; NSF of Hunan Province[09JJ3002]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000273250300018
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10653
专题	中国科学院数学与系统科学研究院
通讯作者	Xiao, Aiguo
作者单位	1.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China 2.Acad Sinica, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Ding, Zhiqing,Xiao, Aiguo,Li, Min. Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2010,233(8):1905-1914.
APA	Ding, Zhiqing,Xiao, Aiguo,&Li, Min.(2010).Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,233(8),1905-1914.
MLA	Ding, Zhiqing,et al."Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 233.8(2010):1905-1914.