A New Stable Algorithm to Compute Hankel Transform Using Chebyshev Wavelets

作者：Pandey Rajesh K; Singh Vineet K; Singh Om P^*

来源：Communications in Computational Physics, 2010, 8(2): 351-373.

DOI：10.4208/cicp.050609.211209a

• Hankel transforms
• Bessel functions
• Chebyshev wavelets
• random noise term

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 v > -1. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms epsilon theta(i) added to the data function f(1), 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.

• 出版日期2010-8