Efficient algorithms to compute Hankel transforms using wavelets

Abstract

The aim of the paper is to propose two efficient algorithms for the numerical evaluation of Hankel transform of order ν, ν > - 1 using Legendre and rationalized Haar (RH) wavelets. The philosophy behind the algorithms is to replace the part x f (x) of the integrand by its wavelet decomposition obtained by using Legendre wavelets for the first algorithm and RH wavelets for the second one, thus representing Fν (y) as a Fourier-Bessel series with coefficients depending strongly on the input function x f (x) in both the cases. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithms. © 2008 Elsevier B.V. All rights reserved.