COLLOCATION METHODS FOR GENERAL VOLTERRA FUNCTIONAL INTEGRAL EQUATIONS WITH VANISHING DELAYS

被引：24
|
作者：
Xie, Hehu [1 ,2 ]
Zhang, Ran [3 ]
Brunner, Hermann [4 ,5 ]
机构：
[1] Chinese Acad Sci, LSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[2] Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[3] Jilin Univ, Sch Math, Changchun 130012, Peoples R China
[4] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
[5] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2011年 / 33卷 / 06期
基金：
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词：
Volterra functional integral equations; vanishing delays; pantograph-type delays; existence and regularity of solutions; collocation solutions; optimal order of convergence; PANTOGRAPH-TYPE;
D O I：
10.1137/100818595
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We analyze the existence, uniqueness, and regularity properties of solutions for general Volterra functional integral equations with the delay function theta(t) vanishing at the initial point of the given interval [0, T] (with theta(t) = qt, 0 < q < 1, representing an important special case). The focus of the paper is then on the the attainable order of convergence, and the question of possible superconvergence, for collocation solutions in certain piecewise polynomial spaces. Numerical experiments complement the theoretical convergence results.
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页码：3303 / 3332
页数：30
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