On the numerical solution of weakly singular integral equations of the first kind using a regularized projection method

被引：0

作者：

Bechouat, Tahar ^{[1
]}

Boussetila, Nadjib ^{[2
]}

机构：

[1] Mohammed Cher Messaadia Univ, Fac Sci & Technol, Dept Math & Informat, BP 1553, Souk Ahras 41000, Algeria

[2] Univ 8 Mai 1945 Guelma, Dept Math, Guelma, Algeria

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2024年 / 101卷 / 05期

关键词：

Ill-posed problems; Tikhonov regularization; Legendre polynomials; Gauss-Jacobi quadrature; weakly singular integral equations; COLLOCATION METHODS; INTEGRODIFFERENTIAL EQUATION; 2ND KIND;

D O I：

10.1080/00207160.2024.2358119

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study investigates a numerical method based on the Jacobi-Gauss quadrature for solving Fredholm integral equations of the first kind with a weakly singular kernel by combining the Tikhonov regularization and projection methods. This numerical method reduces the solution of the weakly singular integral equations of the first kind to the solution of a linear system of algebraic equations. The theoretical analysis of the proposed technique is provided. Finally, several tests are presented to show the validity and efficiency of this approach.

引用

页码：561 / 576

页数：16

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