A new stable algorithm to compute hankel transform using chebyshev wavelets

Abstract

A new stable numerical method, based on Chebyshev wavelets for numerical evaluation of Hankel transform, is proposed in this paper. The Chebyshev wavelets are used as a basis to expand a part of the integrand, r f (r), appearing in the Hankel transformintegral. This transforms theHankel transformintegral into a Fourier-Bessel series. By truncating the series, an efficient and stable algorithm is obtained for the numerical evaluations of the Hankel transforms of order V >.1. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms εθi added to the data function f (r), where θi is a uniform random variable with values in [.1,1]. Finally, an application of the proposed method is given for solving the heat equation in an infinite cylinder with a radiation condition. © 2010 Global-Science Press.