Efficient algorithms to compute Hankel transforms using wavelets |
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Authors: | Vineet K. Singh Rajesh K. Pandey |
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Affiliation: | Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi 221005, India |
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Abstract: | The aim of the paper is to propose two efficient algorithms for the numerical evaluation of Hankel transform of order ν, ν>−1 using Legendre and rationalized Haar (RH) wavelets. The philosophy behind the algorithms is to replace the part xf(x) of the integrand by its wavelet decomposition obtained by using Legendre wavelets for the first algorithm and RH wavelets for the second one, thus representing Fν(y) as a Fourier-Bessel series with coefficients depending strongly on the input function xf(x) in both the cases. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithms. |
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Keywords: | Bessel functions Finite Hankel transform Fourier-Bessel series Legendre wavelets Rationalized Haar wavelets |
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