Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN EFFICIENT AND STABLE ALGORITHM FOR NUMERICAL EVALUATION OF HANKEL TRANSFORMS

  • Singh, Om P. (Department of Applied Mathematics, Institute of Technology, Banaras Hindu University) ;
  • Singh, Vineet K. (Birla Institute of Technology and Science-Pilani, Goa Campus, PDPM Indian Institute of Information Technology, Design and Manufacturing) ;
  • Pandey, Rajesh K. (Birla Institute of Technology and Science-Pilani, Goa Campus, PDPM Indian Institute of Information Technology, Design and Manufacturing)
  • Received : 2009.09.28
  • Accepted : 2009.11.25
  • Published : 2010.09.30
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Abstract

Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.

Keywords

References

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