A stable algorithm for Hankel transforms using hybrid of Block-pulse and Legendre polynomials

A new numerical method, based on hybrid of Block-pulse and Legendre polynomials for numerical evaluation of Hankel transform is proposed in this paper. Hybrid of Block-pulse and Legendre polynomials are used as a basis to expand a part of the integrand, rf(r)rf(r), appearing in the Hankel transform integral. Thus transforming the integral into a Fourier–Bessel series. Truncating the series, an efficient algorithm is obtained for the numerical evaluations of the Hankel transforms of order ν>−1ν>−1. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms εθiεθi added to the data function f(r)f(r), where θiθi is a uniform random variable with values in [−1,1][−1,1]. Finally, an application of the proposed method is given in solving the heat equation in an infinite cylinder with a radiation condition.