Efficient algorithms to compute Hankel transforms using wavelets Original Research Article

The aim of the paper is to propose two efficient algorithms for the numerical evaluation of Hankel transform of order ν, image using Legendre and rationalized Haar (RH) wavelets. The philosophy behind the algorithms is to replace the part image 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 image as a Fourier–Bessel series with coefficients depending strongly on the input function image in both the cases. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithms.