Solvability of Quadratic Integral Equations with Singular Kernel

被引：9
|
作者：
Abdel-Aty, M. A. [1 ,2 ]
Abdou, M. A. [1 ,2 ]
Soliman, A. A. [1 ,2 ]
机构：
[1] Benha Univ, Banha, Egypt
[2] Alexandria Univ, Alexandria, Egypt
来源：
JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES | 2022年 / 57卷 / 01期
基金：
中国国家自然科学基金;
关键词：
singular quadratic integral equation; Banach space; fixed point theorem; logarithmic function; Chebyshev polynomial; NUMERICAL-SOLUTION; 2ND KIND; COLLOCATION METHOD; POLYNOMIALS;
D O I：
10.3103/S1068362322010022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we discuss the existence and uniqueness of solution of the singular quadratic integral equation (SQIE). The Fredholm integral term is assumed in position with singular kernel. Under certain conditions and new discussions, the singular kernel will tend to a logarithmic kernel. Then, using Chebyshev polynomial, a main of spectral relationships are stated and used to obtain the solution of the singular quadratic integral equation with the logarithmic kernel and a smooth kernel. Finally, the Fredholm integral equation of the second kind is established and its solution is discussed, also numerical results are obtained and the error, in each case, is computed.
引用
收藏
页码：12 / 25
页数：14
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