Superconvergence of the composite Simpson's rule for a certain finite-part integral and its applications

doi:10.1016/j.cam.2008.02.001

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	Superconvergence of the composite Simpson's rule for a certain finite-part integral and its applications
	Zhang, Xiaoping 1; Wu, Jiming 2; Yu, Dehao 1
	2009-01-15
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	223 期号:2 页码:598-613
摘要	The superconvergence phenomenon of the composite Simpson's rule for the finite-part integral with a third-order singularity is studied. The superconvergence points are located and the superconvergence estimate is obtained. Some applications of the superconvergence result, including the evaluation of the finite-part integrals and the solution of a certain finite-part integral equation, are also discussed and two algorithms are suggested. Numerical experiments are presented to confirm the superconvergence analysis and to show the efficiency of the algorithms. (C) 2008 Elsevier B.V. All rights reserved.
关键词	Finite-part integral Finite-part integral equation Composite Simpson's rule Superconvergence
DOI	10.1016/j.cam.2008.02.001
语种	英语
资助项目	National Basic Research Program of China[2005CB321701] ; National Natural Science Foundation of China[10531080] ; National Natural Science Foundation of China[10671025] ; Natural Science Foundation of Beijing[1072009]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000261898900008
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/8795
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Xiaoping
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100080, Peoples R China 2.Inst Appl Phys & Computat Math, Lab Computat Phys, Beijing 100088, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Xiaoping,Wu, Jiming,Yu, Dehao. Superconvergence of the composite Simpson's rule for a certain finite-part integral and its applications[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2009,223(2):598-613.
APA	Zhang, Xiaoping,Wu, Jiming,&Yu, Dehao.(2009).Superconvergence of the composite Simpson's rule for a certain finite-part integral and its applications.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,223(2),598-613.
MLA	Zhang, Xiaoping,et al."Superconvergence of the composite Simpson's rule for a certain finite-part integral and its applications".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 223.2(2009):598-613.