A novel computational hybrid approach in solving Hankel transform

摘要

In this paper, we use a combination of Taylor and block-pulse functions on the interval [0, 1], that is called Hybrid Functions to estimate fast and stable solution of Hankel transform. First hybrid of Block-Pulse and Taylor polynomial basis is obtained and orthonormalized using Gram–Schmidt process which are used as basis to expand a part of the integrand,rf(r) appearing in the Hankel transform integral. Thus transforming the integral into a Fourier–Bessel series. Truncating the series, an efficient stable algorithm is obtained for the numerical evaluation of the Hankel transforms of order. The novelty of our method is that we give error analysis and stability of the hybrid algorithm and corroborate our theoretical findings by various numerical experiments for the first time. The solutions obtained by projected method indicate that the approach is easy to implement and computationally very attractive.