NUMERICAL METHODS OF OPTIMAL ACCURACY FOR WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS

被引：8

作者：

Boykov, I. V. ^{[1
]}

Tynda, A. N. ^{[1
]}

机构：

[1] Penza State Univ, Dept Higher & Appl Math, 40 Krasnaya St, Penza 440026, Russia

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2015年 / 6卷 / 04期

关键词：

Babenko and Kolmogorov n-widths; Volterra integral equation; optimal approximation; weakly singular kernel; collocation method;

D O I：

10.15352/afa/06-4-114

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Weakly singular Volterra integral equations of the different types are considered. The construction of accuracy-optimal numerical methods for one-dimensional and multidimensional equations is discussed. Since this question is closely related with the optimal approximation problem, the orders of the Babenko and Kolmogorov n widths of compact sets from some classes of functions have been evaluated. In conclusion we adduce some numerical illustrations for 2-D Volterra equations.

引用

页码：114 / 133

页数：20

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