APPROXIMATION OF WEAKLY SINGULAR NON-LINEAR VOLTERRA-URYSOHN INTEGRAL EQUATIONS BY PIECEWISE POLYNOMIAL PROJECTION METHODS BASED ON GRADED MESH

被引：3

作者：

Nigam, Ritu ^{[1
]}

Kant, Kapil ^{[2
]}

Kumar, B. V. Rathish ^{[2
]}

Nelakanti, Gnaneshwar ^{[1
]}

机构：

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, India

[2] ABV Indian Inst Informat Technol & Management, Dept Appl Sci, Gwalior 474015, India

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2023年 / 13卷 / 03期

关键词：

Superconvergence results; Volterra integral equations with weakly singular kernel; Galerkin method; Multi-Galerkin method; piecewise polynomials; COLLOCATION METHOD; 2ND KIND;

D O I：

10.11948/20220147

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we address the approximation solution of Volterra-Urysohn integral equations which involves weakly singular kernels. In order to get better convergence rates, projection methods namely Galerkin and multi Galerkin methods, along with their iterated versions are used in the space of piecewise polynomials subspaces based on the graded mesh. In addition, we compute the superconvergence results for the proposed integral equation and show that iterated Galerkin method outperforms Galerkin method in terms of order of convergence. Further, we demonstrate numerical examples to verify the proposed theoretical framework.

引用

页码：1359 / 1387

页数：29

共 39 条

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