A New Stable Algorithm to Compute Hankel Transform Using Chebyshev Wavelets
Rajesh K. Pandey 1, Vineet K. Singh 2, Om P. Singh 3*1 PDPM Indian Institute of Information Technology Design and Manufacturing, Jabalpur, India.
2 Birla Institute of Technology and Science-Pilani, Goa Campus, Goa, India.
3 Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi, India.
Received 5 June 2009; Accepted (in revised version) 21 December 2009
Available online 12 March 2010
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, $rf(r)$, 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 $\nu > -1$. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms $\varepsilon \theta_i$ added to the data function $f(r)$, where $\theta_i$ 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.
AMS subject classifications: 65R10
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Key words: Hankel transforms, Bessel functions, Chebyshev wavelets, random noise term.
Email: firstname.lastname@example.org (R. K. Pandey), email@example.com (O. P. Singh), firstname.lastname@example.org (V. K. Singh)