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

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, image, 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 image. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms image added to the data function image, where image is a uniform random variable with values in image. Finally, an application of the proposed method is given in solving the heat equation in an infinite cylinder with a radiation condition.