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),appe...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>−1.The method is quite accurate and stable,as illustrated by given numerical examples with varying degree of random noise terms εθ_(i) added to the data function f(r),where θ_(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.展开更多
文摘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>−1.The method is quite accurate and stable,as illustrated by given numerical examples with varying degree of random noise terms εθ_(i) added to the data function f(r),where θ_(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.
