Approximation to Logarithmic-Cauchy Type Singular Integrals with Highly Oscillatory Kernels

被引：4
|
作者：
Saira [1 ]
Xiang, Shuhuang [1 ]
机构：
[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
来源：
SYMMETRY-BASEL | 2019年 / 11卷 / 06期
基金：
美国国家科学基金会;
关键词：
Clenshaw-Curtis quadrature; steepest descent method; logarithmic singularities; Cauchy singularity; highly oscillatory integrals; CLENSHAW-CURTIS RULES; NUMERICAL-SOLUTION; QUADRATURE; COMPUTATION; EQUATIONS;
D O I：
10.3390/sym11060728
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, a fast and accurate numerical Clenshaw-Curtis quadrature is proposed for the approximation of highly oscillatory integrals with Cauchy and logarithmic singularities, . This method consists of evaluation of the modified moments by stable recurrence relation and Cauchy kernel is solved by steepest descent method that transforms the oscillatory integral into the sum of line integrals. Later theoretical analysis and high accuracy of the method is illustrated by some examples.
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页数：13
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