Volume 8, Issue 2
A New Stable Algorithm to Compute Hankel Transform Using Chebyshev Wavelets

Rajesh K. Pandey, Vineet K. Singh & Om P. Singh

Commun. Comput. Phys., 8 (2010), pp. 351-373.

Published online: 2010-08

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  • 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 θis 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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@Article{CiCP-8-351, author = {}, title = {A New Stable Algorithm to Compute Hankel Transform Using Chebyshev Wavelets}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {2}, pages = {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 θis 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.050609.211209a}, url = {http://global-sci.org/intro/article_detail/cicp/7576.html} }
TY - JOUR T1 - A New Stable Algorithm to Compute Hankel Transform Using Chebyshev Wavelets JO - Communications in Computational Physics VL - 2 SP - 351 EP - 373 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.050609.211209a UR - https://global-sci.org/intro/article_detail/cicp/7576.html KW - AB -

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 θis 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.

Rajesh K. Pandey, Vineet K. Singh & Om P. Singh. (2020). A New Stable Algorithm to Compute Hankel Transform Using Chebyshev Wavelets. Communications in Computational Physics. 8 (2). 351-373. doi:10.4208/cicp.050609.211209a
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