AN EFFICIENT ALGORITHM FOR EVALUATION OF OSCILLATORY INTEGRALS HAVING CAUCHY AND JACOBI TYPE SINGULARITY KERNELS

Herein, an algorithm for efficient evaluation of oscillatory Fourier-integrals with Jacobi-Cauchy type singularities is suggested. This method is based on the use of the traditional Clenshaw-Curtis (CC) algorithms in which the given function is approximated by the truncated Cheby-shev series, term by term, and the oscillatory factor is approximated by using Bessel function of the first kind. Subsequently, the modified moments are computed efficiently using the numerical steepest descent method or special functions. Furthermore, Algorithm and programming code in MATHEMATICA® 9.0 are provided for the implementation of the method for automatic computation on a computer. Finally, selected numerical ex-amples are given in support of our theoretical analysis. © 2022 KSCAM