FAST APPROXIMATION OF ALGEBRAIC AND LOGARITHMIC HYPERSINGULAR TYPE SINGULAR INTEGRALS WITH HIGHLY OSCILLATORY KERNEL

被引：1

作者：

Kayijuka, Idrissa ^{[1
]}

Ege, Serife Muge ^{[1
]}

Konuralp, Ali ^{[2
]}

Topal, Fatma Serap ^{[1
]}

机构：

[1] Ege Univ, Dept Math, Izmir, Turkey

[2] Manisa Celal Bayar Univ, Dept Math, Manisa, Turkey

来源：

INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS | 2020年 / 18卷 / 06期

关键词：

highly oscillatory kernel; Gauss quadrature; hypersingular integrals; Chebyshev and modified Chebyshev algorithms; algebraic and logarithm singular integrals; CAUCHY PRINCIPAL VALUE; ORTHOGONAL POLYNOMIALS; EQUATIONS; QUADRATURE;

D O I：

10.28924/2291-8639-18-2020-965

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Herein, highly oscillatory integrals with hypersingular type singularities are studied. After transforming the original integral into a sum of line integrals over a positive semi-infinite interval, a Gauss-related quadrature rule is constructed. The vehicle utilized is the moment's information. The comparison of two algorithms (Chebyshev and its modified one) to produce the recursion coefficients that satisfy orthogonal polynomial with respect to Gautschi logarithmic weight function, is investigated. Lastly, numerical examples are given to substantiate the effectiveness of the proposed method.

引用

页码：965 / 980

页数：16

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