Table of Contents
International Journal of Analysis
Volume 2014, Article ID 670562, 11 pages
http://dx.doi.org/10.1155/2014/670562
Research Article

Stable Numerical Evaluation of Finite Hankel Transforms and Their Application

1Department of Mathematical Sciences, Indian Institute of Technology, Banaras Hindu University, Varanasi 221005, India
2Department of Mathematics, Udai Pratap Autonomous College, Varanasi 221002, India
3Department of Mathematics, IEC, College of Engineering & Technology, Greater Noida 201306, India

Received 1 June 2014; Revised 21 September 2014; Accepted 23 September 2014; Published 13 November 2014

Academic Editor: Baruch Cahlon

Copyright © 2014 Manoj P. Tripathi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new stable algorithm, based on hat functions for numerical evaluation of Hankel transform of order , is proposed in this paper. The hat basis functions are used as a basis to expand a part of the integrand, , appearing in the Hankel transform integral. This leads to a very simple, efficient, and stable algorithm for the numerical evaluation of Hankel transform. The novelty of our paper is that we give error and stability analysis of the algorithm and corroborate our theoretical findings by various numerical experiments. Finally, an application of the proposed algorithm is given for solving the heat equation in an infinite cylinder with a radiation condition.