Limit values of derivatives of the cauchy integrals and computation of the logarithmic potentials

doi:10.1007/s00607-003-0072-4

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	Limit values of derivatives of the cauchy integrals and computation of the logarithmic potentials
	Xu, Y ; Chen, HL ; Zou, Q
	2004-11-01
发表期刊	COMPUTING
ISSN	0010-485X
卷号	73 期号:4 页码:295-327
摘要	We derive limit values of high-order derivatives of the Cauchy integrals, which are extensions of the Plemelj-Sokhotskyi formula. We then use them to develop the Taylor expansion of the logarithmic potentials at the normal direction. Based on the Taylor expansion and numerical integration methods for weekly singular functions using grid points, we design fast algorithms for computing the logarithmic potentials. We prove that these methods have an optimal order of convergence with a linear computational complexity. Numerical examples are included to confirm the theoretical estimates for the methods.
关键词	Cauchy integrals limit values logarithmic potentials singular integrals numerical evaluation of logarithmic potentials
DOI	10.1007/s00607-003-0072-4
语种	英语
WOS研究方向	Computer Science
WOS类目	Computer Science, Theory & Methods
WOS记录号	WOS:000225386400001
出版者	SPRINGER WIEN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19634
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Y
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Syracuse Univ, Dept Math, Syracuse, NY 13244 USA 3.Zhongshan Univ Guangzhou, Dept Comp Sci & Comp Applicat, Guangzhou 510275, Peoples R China
推荐引用方式 GB/T 7714	Xu, Y,Chen, HL,Zou, Q. Limit values of derivatives of the cauchy integrals and computation of the logarithmic potentials[J]. COMPUTING,2004,73(4):295-327.
APA	Xu, Y,Chen, HL,&Zou, Q.(2004).Limit values of derivatives of the cauchy integrals and computation of the logarithmic potentials.COMPUTING,73(4),295-327.
MLA	Xu, Y,et al."Limit values of derivatives of the cauchy integrals and computation of the logarithmic potentials".COMPUTING 73.4(2004):295-327.