A New Stable Algorithm to Compute Hankel Transform Using Chebyshev Wavelets (Communications in Computational Physics, 2010)
A new stable numerical method, based on Chebyshev wavelets for numericalevaluation of Hankel transform, is proposed in this paper. The Chebyshev waveletsare used as a basis to expand a part of the integrand, r f(r), appearing in the Hankeltransform integral. This transforms the Hankel transform integral into a Fourier-Besselseries. By truncating the series, an efficient and stable algorithm is obtained for the numericalevaluations of the Hankel transforms of order ν > −1. The method is quiteaccurate and stable, as illustrated by given numerical examples with varying degree ofrandom noise terms εθi added to the data function f(r), where θi is a uniform randomvariable with values in [−1,1]. Finally, an application of the proposed method is givenfor solving the heat equation in an infinite cylinder with a radiation condition.