The superconvergence of composite Newton-Cotes rules for Hadamard finite-part integral on a circle
文献类型：期刊论文
| 作者 | Zhang, Xiaoping1,3; Wu, Jiming2; Yu, Dehao1 |
| 刊名 | COMPUTING
 |
| 出版日期 | 2009-07-01 |
| 卷号 | 85期号:3页码:219-244 |
| 关键词 | Hadamard finite-part integral Composite Newton-Cotes rule Superconvergence Clausen function |
| ISSN号 | 0010-485X |
| DOI | 10.1007/s00607-009-0048-5 |
| 英文摘要 | We study the general (composite) Newton-Cotes rules for the computation of Hadamard finite-part integral on a circle with the hypersingular kernel sin(-2) x-s/2 and focus on their pointwise superconvergence phenomenon, i.e., when the singular point coincides with some a priori known point, the convergence rate is higher than what is globally possible. We show that the superconvergence rate of the (composite) Newton-Cotes rules occurs at the zeros of a special function Phi(k)(tau) and prove the existence of the superconvergence points. The relation between Phi(k)(tau) and S(k)(tau) defined in Wu and Sun (Numer Math 109: 143-165, 2008) is established, and the efficient calculation of Cotes coefficients is also discussed. Several numerical examples are provided to validate the theoretical analysis. |
| 资助项目 | National Basic Research Program of China[2005CB321701] ; National Natural Science Foundation of China[10531080] ; National Natural Science Foundation of China[10871030] ; National Natural Science Foundation of China[10671025] ; Natural Science Foundation of Beijing[1072009] ; Laboratory of Computational Physics. |
| WOS研究方向 | Computer Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000267824200003 |
| 出版者 | SPRINGER WIEN |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/8262]  |
| 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, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 2.Inst Appl Phys & Computat Math, Lab Computat Phys, Beijing 100088, Peoples R China 3.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhang, Xiaoping,Wu, Jiming,Yu, Dehao. The superconvergence of composite Newton-Cotes rules for Hadamard finite-part integral on a circle[J]. COMPUTING,2009,85(3):219-244. |
| APA | Zhang, Xiaoping,Wu, Jiming,&Yu, Dehao.(2009).The superconvergence of composite Newton-Cotes rules for Hadamard finite-part integral on a circle.COMPUTING,85(3),219-244. |
| MLA | Zhang, Xiaoping,et al."The superconvergence of composite Newton-Cotes rules for Hadamard finite-part integral on a circle".COMPUTING 85.3(2009):219-244. |
入库方式： OAI收割
来源：数学与系统科学研究院
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