A stable algorithm for numerical evaluation of Hankel transforms using Haar wavelets

Abstract

The purpose of the paper is to propose a stable algorithm for the numerical evaluation of the Hankel transform Fn(y) of order n of a function f(x) using Haar wavelets. The integrand √x f(x) is replaced by its wavelet decomposition. Thus representing Fn(y) as a series with coefficients depending strongly on the local behavior of the function √x f(x), thereby getting an efficient and stable algorithm for their numerical evaluation. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithm. © 2009 Springer Science+Business Media, LLC.