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

共 50 条

[21] APPROXIMATION ORDER OF SINGULAR INTEGRALS WITH A LOGARITHMIC-POWER SINGULARITY
SHESHKO, MA
DOKLADY AKADEMII NAUK BELARUSI, 1976, 20 (11): : 975 - 976
[22] Efficient quadrature of highly oscillatory integrals with algebraic singularities
Kang, Hongchao
Xiang, Shuhuang
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 237 (01) : 576 - 588
[23] ON AN ASYMPTOTIC FORMULA FOR A TYPE OF SINGULAR OSCILLATORY INTEGRALS
WANG, XH
CHOU, YS
KEXUE TONGBAO, 1983, 28 (04): : 570 - 570
[24] Efficient computation of highly oscillatory integrals with Hankel kernel
Xu, Zhenhua
Milovanovic, Gradimir V.
Xiang, Shuhuang
APPLIED MATHEMATICS AND COMPUTATION, 2015, 261 : 312 - 322
[25] ON AN ASYMPTOTIC FORMULA FOR A TYPE OF SINGULAR OSCILLATORY INTEGRALS
王兴华
周蕴时
Science Bulletin, 1983, (04) : 570 - 570
[26] AN ASYMPTOTIC FORMULA FOR A TYPE OF SINGULAR OSCILLATORY INTEGRALS
HSU, LC
CHOU, YS
MATHEMATICS OF COMPUTATION, 1981, 37 (156) : 503 - 507
[27] Numerical approximations to integrals with a highly oscillatory Bessel kernel
Chen, Ruyun
APPLIED NUMERICAL MATHEMATICS, 2012, 62 (05) : 636 - 648
[28] Quadrature rules and asymptotic expansions for two classes of oscillatory Bessel integrals with singularities of algebraic or logarithmic type
Kang, Hongchao
Ma, Junjie
APPLIED NUMERICAL MATHEMATICS, 2017, 118 : 277 - 291
[29] Fast computation of a class of highly oscillatory integrals
Chen, Ruyun
APPLIED MATHEMATICS AND COMPUTATION, 2014, 227 : 494 - 501
[30] On the asymptotic order of Filon-type methods for highly oscillatory integrals with an algebraic singularity
Mo, Hongmin
Xiang, Shuhuang
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (22) : 9105 - 9110

← 1 2 3 4 5 →