A New Stable Algorithm to Compute Hankel Transform Using Chebyshev Wavelets
Year: 2010
Author: Rajesh K. Pandey, Vineet K. Singh, Om P. Singh
Communications in Computational Physics, Vol. 8 (2010), Iss. 2 : pp. 351–373
Abstract
A new stable numerical method, based on Chebyshev wavelets for numerical evaluation of Hankel transform, is proposed in this paper. The Chebyshev wavelets are used as a basis to expand a part of the integrand, r f(r), appearing in the Hankel transform integral. This transforms the Hankel transform integral into a Fourier-Bessel series. By truncating the series, an efficient and stable 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 εθi 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 for solving the heat equation in an infinite cylinder with a radiation condition.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.050609.211209a
Communications in Computational Physics, Vol. 8 (2010), Iss. 2 : pp. 351–373
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Author Details
Rajesh K. Pandey Email
Vineet K. Singh Email
Om P. Singh Email
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