Open AccessOn Computation of Highly Oscillatory Integrals with Bessel Kernel
Author(s) -
Muhammad Munib Khan,
Sakhi Zaman
Publication year - 2019
Publication title -
earthline journal of mathematical sciences
Language(s) - English
Resource type - Journals
ISSN - 2581-8147
DOI - 10.34198/ejms.3120.5163
Subject(s) - laguerre polynomials , bessel function , mathematics , trigonometric integral , kernel (algebra) , quadrature (astronomy) , fourier transform , computation , mathematical analysis , gauss , bessel process , numerical integration , cylindrical harmonics , fourier series , orthogonal polynomials , algorithm , pure mathematics , physics , gegenbauer polynomials , trigonometry , optics , classical orthogonal polynomials , quantum mechanics
In this paper, we introduce a new numerical scheme for approximation of highly oscillatory integrals having Bessel kernel. We transform the given integral to a special form having improper nonoscillatory Laguerre type and proper oscillatory integrals with Fourier kernels. Integrals with Laguerre weights over [0, ∞) will be solved by Gauss-Laguerre quadrature and oscillatory integrals with Fourier kernel can be evaluated by meshless-Levin method. Some numerical examples are also discussed to check the efficiency of proposed method.