Fast Approximation of Algebraic and Logarithmic Hypersingular Type Singular Integrals with Highly Oscillatory Kernel
Articles > Article · 2020
Authors: Idrissa Kayijuka, Åžerife Müge Ege, Ali Konuralp, Fatma Serap Topal
International Journal of Analysis and Applications, International, Scopus, 2020
DOI: 10.28924/2291-8639-18-2020-965
Summary
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.