KMS Of Academy of mathematics and systems sciences, CAS
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. |
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