Optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays
文献类型：期刊论文
| 作者 | Brunner, H; Hu, QY
|
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2005 |
| 卷号 | 43期号:5页码:1934-1949 |
| 关键词 | delay integral equation proportional delays collocation method iterated collocation solution optimal order of superconvergence |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/040615705 |
| 英文摘要 | In this paper we analyze the optimal convergence properties of collocation approximations to solutions of Volterra integral equations of the second kind with vanishing variable delays. The focus of the analysis is on the superconvergence of the (iterated) collocation approximation corresponding to collocation in the space of (discontinuous) piecewise polynomials of degree m-1 >= 0. We show that on uniform meshes the iterated collocation solution possesses the global superconvergence order m + 1, and that the solution's order of local superconvergence at the nodes of the underlying mesh cannot exceed m + 2, in sharp contrast to problems with nonvanishing delays. Moreover, the optimal order p* = m + 2 can be attained only under suitable assumptions. This result also resolves a conjecture of 1997 regarding the attainable order of local superconvergence for Volterra integral equations containing a proportional delay qt with q is an element of (0, 1). |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000234470800007 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1530]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Brunner, H |
| 作者单位 | 1.Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Brunner, H,Hu, QY. Optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2005,43(5):1934-1949. |
| APA | Brunner, H,&Hu, QY.(2005).Optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays.SIAM JOURNAL ON NUMERICAL ANALYSIS,43(5),1934-1949. |
| MLA | Brunner, H,et al."Optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays".SIAM JOURNAL ON NUMERICAL ANALYSIS 43.5(2005):1934-1949. |
入库方式： OAI收割
来源：数学与系统科学研究院
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