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

Abstract

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, r f (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 > - 1. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms ε θi 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. © 2009 Elsevier B.V. All rights reserved.