Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals

doi:10.1016/j.cam.2009.11.029

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	Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals
	Li, Jin 2; Zhang, Xiaoping 1; Yu, Dehao 2
	2010-04-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	233 期号:11 页码:2841-2854
摘要	In this article, the general (composite) Newton-Cotes rules for evaluating Hadamard finite-part integrals with third-order singularity (which is also called "supersingular integrals") are investigated and the emphasis is placed on their pointwise superconvergence and ultraconvergence. The main error of the general Newton-Cotes rules is derived, which is shown to be determined by a certain function s(k)'(tau). Based on the error expansion, the corresponding modified quadrature rules are also proposed. At last, some numerical experiments are carried out to validate the theoretical analysis. (C) 2009 Elsevier B.V. All rights reserved.
关键词	Supersingular integral Composite Newton-Cotes rule Superconvergence Ultraconvergence
DOI	10.1016/j.cam.2009.11.029
语种	英语
资助项目	National Basic Research Program of China[2005CB321701] ; National Natural Science Foundation of China[10531080] ; Natural Science Foundation of Beijing[1072009]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000275251600008
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/9976
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.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China 2.CAS, LSEC, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Jin,Zhang, Xiaoping,Yu, Dehao. Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2010,233(11):2841-2854.
APA	Li, Jin,Zhang, Xiaoping,&Yu, Dehao.(2010).Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,233(11),2841-2854.
MLA	Li, Jin,et al."Superconvergence and ultraconvergence of Newton-Cotes rules for supersingular integrals".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 233.11(2010):2841-2854.