The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals

doi:10.1016/j.cam.2010.06.023

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	The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals
	Liu, Dongjie 3; Wu, Jiming 1; Yu, Dehao 2
	2010-12-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	235 期号:3 页码:696-707
摘要	We consider the general (composite) Newton-Cotes method for the computation of Cauchy principal value integrals and focus on its pointwise superconvergence phenomenon, which means that the rate of convergence of the Newton-Cotes quadrature rule is higher than what is globally possible when the singular point coincides with some a priori known point. The necessary and sufficient conditions satisfied by the superconvergence point are given. Moreover, the superconvergence estimate is obtained and the properties of the superconvergence points are investigated. Finally, some numerical examples are provided to validate the theoretical results. (C) 2010 Elsevier B.V. All rights reserved.
关键词	Cauchy principal value integral Newton-Cotes method Superconvergence result
DOI	10.1016/j.cam.2010.06.023
语种	英语
资助项目	Shanghai Leading Academic Discipline Project[J50101] ; Shanghai Municipality[B.37-0101-08-013] ; National Natural Science Foundation of China[10871030] ; National Natural Science Foundation of China[10531080] ; Laboratory of Computational Physics ; National Basic Research Program of China[2005CB321701]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000282394500014
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/9316
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, Jiming
作者单位	1.Inst Appl Phys & Computat Math, Lab Computat Phys, Beijing 100088, Peoples R China 2.CAS, Acad Math & Syst Sci, LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 3.Shanghai Univ, Dept Math, Coll Sci, Shanghai 200444, Peoples R China
推荐引用方式 GB/T 7714	Liu, Dongjie,Wu, Jiming,Yu, Dehao. The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2010,235(3):696-707.
APA	Liu, Dongjie,Wu, Jiming,&Yu, Dehao.(2010).The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,235(3),696-707.
MLA	Liu, Dongjie,et al."The superconvergence of the Newton-Cotes rule for Cauchy principal value integrals".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 235.3(2010):696-707.