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A stable algorithm for numerical evaluation of Hankel transforms using Haar wavelets

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Abstract

The purpose of the paper is to propose a stable algorithm for the numerical evaluation of the Hankel transform F n (y) of order n of a function f(x) using Haar wavelets. The integrand \(\sqrt x f(x)\) is replaced by its wavelet decomposition. Thus representing F n (y) as a series with coefficients depending strongly on the local behavior of the function \(\sqrt x f(x)\), thereby getting an efficient and stable algorithm for their numerical evaluation. Numerical evaluations of test functions with known analytical Hankel transforms illustrate the proposed algorithm.

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Authors and Affiliations

  1. Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi, 221005, India

    Rajesh K. Pandey, Om Prakash Singh & Vineet K. Singh

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  1. Rajesh K. Pandey
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  2. Om Prakash Singh
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  3. Vineet K. Singh
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Correspondence to Om Prakash Singh.

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Pandey, R.K., Singh, O.P. & Singh, V.K. A stable algorithm for numerical evaluation of Hankel transforms using Haar wavelets. Numer Algor 53, 451–466 (2010). https://doi.org/10.1007/s11075-009-9313-0

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  • DOI: https://doi.org/10.1007/s11075-009-9313-0

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