@article{SAIRA2025, 
author = { SAIRA and Wenxiu Ma and Suliman Khan},
title = {An efficient numerical method for highly oscillatory logarithmic-algebraic singular integrals},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {4899-4914},
keywords = {algebraic singularities, logarithmic singularity, high oscillations, analytic function, Gauss-Laguerre quadrature},
url = {https://www.sciopen.com/article/10.3934/math.2025224},
doi = {10.3934/math.2025224},
abstract = {This paper discussed the numerical evaluation of highly oscillatory integrals involving logarithmic and algebraic singularities. For an analytic function in a sufficiently large region containing    [  a  ,  b  ], the integral was transformed into the sum of two line integrals where the integrands did not oscillate and decay exponentially. Thus, to approximate the line integrals, generalized Gauss-Laguerre quadrature and logarithmic Gauss-Laguerre quadrature were applied. The error bound and numerical results demonstrated that the proposed method efficiently obtained high-precision results even for high oscillations.}
}