Optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays

doi:10.1137/040615705

	Optimal superconvergence orders of iterated collocation solutions for volterra integral equations with vanishing delays
	Brunner, H ; Hu, QY
	2005
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	43 期号:5 页码:1934-1949
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).
关键词	delay integral equation proportional delays collocation method iterated collocation solution optimal order of superconvergence
DOI	10.1137/040615705
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000234470800007
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1531
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.