The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application

doi:10.1080/00207160802226517

CSpace

	The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application
	Zhang, Xiaoping 1; Wu, Jiming 2; Yu, Dehao 1
	2010
发表期刊	INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN	0020-7160
卷号	87 期号:4 页码:855-876
摘要	The quadrature method for Hadamard finite-part integral on a circle is discussed and the emphasis is placed on the pointwise superconvergence phenomenon of the composite trapezoidal rule, i.e. when the singular point coincides with some a priori known points, the accuracy can be better than what is globally possible. The existence and uniqueness of the superconvergence points are proved and the correspondent superconvergence estimate is obtained. An indirect method is introduced and then applied to solve the integral equation of the second kind containing finite-part kernels, including that arising in the scattering theory. Some numerical results are also presented to confirm the theoretical results and to show the efficiency of the algorithms.
关键词	finite-part integral composite trapezoidal rule superconvergence finite-part integral equation of the second kind scattering problem
DOI	10.1080/00207160802226517
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:000275825000014
出版者	TAYLOR & FRANCIS 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/9882
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.CAS, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing, 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. The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2010,87(4):855-876.
APA	Zhang, Xiaoping,Wu, Jiming,&Yu, Dehao.(2010).The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,87(4),855-876.
MLA	Zhang, Xiaoping,et al."The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 87.4(2010):855-876.