Numerical Approximation of Rapidly Oscillatory Bessel Integral Transforms

Abstract

We present a new procedure of Levin type which is based on Gaussian radial basis function for evaluation of rapidly oscillating integrals that contains first kind of the Bessel function 􀜬􀯩(􀟱􀝔). Multi-resolution quadrature rules like hybrid and Haar functions are used in the context of Bessel oscillatory integrals as well. Numerical test problems are solved to verify the accuracy and efficiency of the new methods.