Article ID Journal Published Year Pages File Type
4639174 Journal of Computational and Applied Mathematics 2014 10 Pages PDF
Abstract

In this paper, we study the asymptotics and evaluation of the oscillatory Bessel Hilbert transform ⨍0∞f(x)x−τJν(ωx)dx with 0<τ<∞0<τ<∞. The singularity of the Hilbert transform is transferred to an individual oscillatory integral independent of f(x)f(x). For this singular integral, we present two methods. One is the combination of a Filon-type method and a complex integration method, the other is the combination of a Filon-type method and an adaptive Clenshaw–Curtis quadrature. The remaining integral which is nonsingular can be well calculated with a combination of a Filon-type method and a Gauss–Laguerre quadrature. The efficiency and accuracy of the proposed methods are illustrated by numerical examples.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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