DISCRETE SUPERCONVERGENCE OF COLLOCATION SOLUTIONS FOR FIRST-KIND VOLTERRA INTEGRAL EQUATIONS

被引：6

作者：

Liang, Hui ^{[1
]}

Brunner, Hermann ^{[2
,3
]}

机构：

[1] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Heilongjiang, Peoples R China

[2] Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

来源：

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS | 2012年 / 24卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

First-kind Volterra integral equations; collocation solutions; piecewise polynomials; superconvergence at non-mesh points; 1ST KIND; APPROXIMATIONS;

D O I：

10.1216/JIE-2012-24-3-359

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that collocation solutions for first-kind Volterra integral equations based on (discontinuous or continuous) piecewise polynomials cannot exhibit local superconvergence at the points of a uniform mesh. In this paper we present a complete analysis of local superconvergence of such collocation solutions for first-kind Volterra integral equations at non-mesh points. In particular, we discuss (i) the existence of superconvergence points for prescribed collocation points; (ii) the existence of collocation points for prescribed superconvergence points. Numerous examples illustrate the theory.

引用

页码：359 / 391

页数：33

共 12 条

[1]

Binmore K.G., 1982, MATHEMATICAL ANALYSI

[2]

Brunner, 2010, 7 LECTIRES THEORY NU

[3] On the divergence of collocation solutions in smooth piecewise polynomial spaces for Volterra integral equations [J].

Brunner, H .

BIT NUMERICAL MATHEMATICS, 2004, 44 (04) :631-650

[4] COLLOCATION METHODS FOR VOLTERRA INTEGRAL-EQUATIONS OF THE 1ST KIND [J].

BRUNNER, H .

COMPUTING, 1979, 23 (02) :179-187

[5] SUPER-CONVERGENCE OF COLLOCATION METHODS FOR VOLTERRA INTEGRAL-EQUATIONS OF THE 1ST KIND [J].

BRUNNER, H .

COMPUTING, 1979, 21 (02) :151-157

[6]

BRUNNER H, 1978, NUMER MATH, V30, P117, DOI 10.1007/BF02042940

[7]

Brunner H., IMA J NUMER ANAL TO

[8] Discontinuous Galerkin approximations for Volterra integral equations of the first kind [J].

Brunner, Hermann ;

Davies, Penny J. ;

Duncan, Dugald B. .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2009, 29 (04) :856-881

[9]

Eggermont P.P.B., 1986, NUMER MATH, V48, P263

[10]

Eggermont P.P.B., 1982, TREATMENT OF INTEGRA

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