Application of Hankel Transform for Solving a Fracture Problem of a Cracked Piezoelectric Strip Under Thermal Loading

Ueda, Sei

doi:10.5772/36776

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2015

2023

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Cited by 3 publications

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“…Laplace's partial differential equation in cylindrical coordinates can be transformed into an ordinary differential equation by using the Hankel transform. Because the Hankel transform is the two-dimensional Fourier transform of a circularly symmetric function, it plays an important role in optical data processing [5][6][7]. In optics, the Hankel transform appears in many contexts, not the least of which is the propagation of cylindrically symmetric laser beams.…”

Section: Introductionmentioning

confidence: 99%

A Wavelet Algorithm for Fourier-Bessel Transform Arising in Optics

Irfan

Siddiqi

2015

International Journal of Engineering Mathematics

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The aim of the paper is to propose an efficient and stable algorithm that is quite accurate and fast for numerical evaluation of the Fourier-Bessel transform of order ], ] > −1, using wavelets. The philosophy behind the proposed algorithm is to replace the part ( ) of the integral by its wavelet decomposition obtained by using CAS wavelets thus representing ] ( ) as a Fourier-Bessel series with coefficients depending strongly on the input function ( ). The wavelet method indicates that the approach is easy to implement and thus computationally very attractive.

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Section: Introductionmentioning

confidence: 99%