Analysis of collocation solutions for a class of functional equations with vanishing delays

doi:10.1093/imanum/drp051

	Analysis of collocation solutions for a class of functional equations with vanishing delays
	Brunner, Hermann 1,2; Xie, Hehu3 ; Zhang, Ran 4
	2011-04-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	31 期号:2 页码:698-718
摘要	We study the existence, uniqueness and regularity properties of solutions for the functional equation y(t) = b(t)y(theta(t)) + f(t), t is an element of [0, T], where the delay function theta(t) vanishes at t = 0. Functional equations corresponding to the linear delay function theta(t) = qt (0 < q < 1) represent an important special case. We then analyse the optimal order of convergence of piecewise polynomial collocation approximations to solutions of these functional equations. The theoretical results are illustrated by extensive numerical examples.
关键词	functional equation with vanishing delay q-difference equation uniqueness and regularity of solution collocation solutions optimal order of convergence integro-functional equation
DOI	10.1093/imanum/drp051
语种	英语
资助项目	Natural Sciences and Engineering Research Council of Canada[DG A-9406] ; Hong Kong Research Grants Council ; National Nature Science Foundation of China[10801062] ; Jilin University ; K. C. Wong Education Foundation in Hong Kong
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000289166300015
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11491
专题	计算数学与科学工程计算研究所
通讯作者	Brunner, Hermann
作者单位	1.Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada 2.Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China 3.Chinese Acad Sci, Lab Sci & Engn Comp, Inst Computat Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Jilin Univ, Sch Math, Changchun 130012, Peoples R China
推荐引用方式 GB/T 7714	Brunner, Hermann,Xie, Hehu,Zhang, Ran. Analysis of collocation solutions for a class of functional equations with vanishing delays[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2011,31(2):698-718.
APA	Brunner, Hermann,Xie, Hehu,&Zhang, Ran.(2011).Analysis of collocation solutions for a class of functional equations with vanishing delays.IMA JOURNAL OF NUMERICAL ANALYSIS,31(2),698-718.
MLA	Brunner, Hermann,et al."Analysis of collocation solutions for a class of functional equations with vanishing delays".IMA JOURNAL OF NUMERICAL ANALYSIS 31.2(2011):698-718.