The superconvergence of composite trapezoidal rule for Hadamard finite-part integral on a circle and its application | |
Zhang, Xiaoping1; Wu, Jiming2; Yu, Dehao1 | |
刊名 | INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS |
2010 | |
卷号 | 87期号:4页码:855-876 |
关键词 | finite-part integral composite trapezoidal rule superconvergence finite-part integral equation of the second kind scattering problem |
ISSN号 | 0020-7160 |
DOI | 10.1080/00207160802226517 |
英文摘要 | 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. |
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 |
语种 | 英语 |
出版者 | TAYLOR & FRANCIS LTD |
WOS记录号 | WOS:000275825000014 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/9881] |
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. |
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