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


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
doi:10.4208/cicp.050609.211209a

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, $rf(r)$, 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

Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Hankel transforms, Bessel functions, Chebyshev wavelets, random noise term.

*Corresponding author.
Email: wavelet_r@yahoo.co.in (R. K. Pandey), singhom@gmail.com (O. P. Singh), vks1itbhu@gmail.com (V. K. Singh)
 

The Global Science Journal