Optimal superconvergence results for delay integro-differential equations of pantograph type

doi:10.1137/060660357

	Optimal superconvergence results for delay integro-differential equations of pantograph type
	Brunner, Hermann ; Hu, Qiya
	2007
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	45 期号:3 页码:986-1004
摘要	We analyze the optimal ( global and local) orders of superconvergence of collocation solutions u(h) on uniform meshes I(h) for delay Volterra integro-differential equations with proportional delay functions given by theta(t) = qt (0 < q < 1, t epsilon [ 0, T]). In particular, we show that if u(h) is a continuous piecewise polynomial of degree m >= 2, and if collocation is at the Gauss (-Legendre) points, then the ( optimal) order of local superconvergence on I(h) is p* = m + 2. It turns out that the same order p* holds for nonlinear ( strictly increasing) delay functions vanishing at t = 0. However, on judiciously chosen geometric meshes, collocation at the Gauss points yields the order 2m - epsilon(N), where epsilon N -> 0 as the number N of mesh points tends to infinity. Optimal local superconvergence results for the pantograph delay differential equation are obtained as special cases of our general analysis.
关键词	volterra integro-differential equation vanishing delays proportional delays pantograph equation collocation solutions optimal order of superconvergence
DOI	10.1137/060660357
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000247647700005
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/4466
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.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100080, Peoples R China 3.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, Hermann,Hu, Qiya. Optimal superconvergence results for delay integro-differential equations of pantograph type[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2007,45(3):986-1004.
APA	Brunner, Hermann,&Hu, Qiya.(2007).Optimal superconvergence results for delay integro-differential equations of pantograph type.SIAM JOURNAL ON NUMERICAL ANALYSIS,45(3),986-1004.
MLA	Brunner, Hermann,et al."Optimal superconvergence results for delay integro-differential equations of pantograph type".SIAM JOURNAL ON NUMERICAL ANALYSIS 45.3(2007):986-1004.