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 - <p style="text-align: justify;">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 &gt; −1. The method is quite
accurate and stable, as illustrated by given numerical examples with varying degree of
random noise terms εθ<sub>i</sub> added to the data function f(r), where θ<sub>i&nbsp;</sub>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.</p>