Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels

被引：108

作者：

Brunner, H ^{[1
]}

Pedas, A

Vainikko, G

机构：

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

[2] Aalto Univ, Inst Math, FIN-02015 Espoo, Finland

[3] Univ Tartu, Dept Appl Math, EE-50409 Tartu, Estonia

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2001年 / 39卷 / 03期

关键词：

linear weakly singular Volterra integro-differential equations; piecewise polynomial collocation method; graded grids; optimal order of convergence;

D O I：

10.1137/S0036142900376560

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the first part of this paper we study the regularity properties of solutions of linear Volterra integro-differential equations with weakly singular or other nonsmooth kernels. We then use these results in the analysis of two piecewise polynomial collocation methods for solving such equations numerically. The main purpose of the paper is the derivation of optimal global convergence estimates and the analysis of the attainable order of local superconvergence at the collocation points.

引用

页码：957 / 982

页数：26

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