@Article{IJNAM-18-4,
author = {​Idrissa, Kayijuka and Serife, Muge, Ege and Topal, Serap, Fatma and Konuralp, Ali},
title = {Fast Gauss-Related Quadrature for Highly Oscillatory Integrals with Logarithm and Cauchy-Logarithmic Type Singularities},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2021},
volume = {18},
number = {4},
pages = {442--457},
abstract = {<p style="text-align: justify;">This paper presents an efficient method for the computation of two highly oscillatory
integrals having logarithmic and Cauchy-logarithmic singularities. This approach first requires the
transformation of the original oscillatory integrals into a sum of line integrals with semi-infinite
intervals. Afterwards, the coefficients of the three-term recurrence relation that satisfy the orthogonal polynomial are obtained by using the method based on moments, where classical Laguerre
and Gautschi&#39;s logarithmic weight functions are employed. The algorithm reveals that with fixed $n$, the method is capable of achieving significant figures within a short time. Furthermore, the
approach yields higher accuracy as the frequency increases. The results of numerical experiments
are given to substantiate our theoretical analysis.</p>},
issn = {2617-8710},
doi = {https://doi.org/2021-IJNAM-19115},
url = {https://global-sci.com/article/82990/fast-gauss-related-quadrature-for-highly-oscillatory-integrals-with-logarithm-and-cauchy-logarithmic-type-singularities}
}