Stable algorithm for computation of 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. Chebyshev wavelets are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. This transforms the Hankel transform integral into a Fourier-Bessel series. Truncating the series, an efficient, stable algorithm is obtained for the numerical evaluations of the Hankel transforms of order ν>-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 in solving the heat equation in an infinite cylinder with a radiation condition. © 2012 by Nova Science Publishers, Inc. All rights reserved.