On Computation of Highly Oscillatory Integrals with Bessel Kernel

Abstract

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.