Article ID Journal Published Year Pages File Type
4638920 Journal of Computational and Applied Mathematics 2014 11 Pages PDF
Abstract

In this paper, we study efficient methods for computing the integrals of the form ∫01xa(1−x)bf(x)Jv(ωx)dx, where a,b,v,ωa,b,v,ω are the given constants and ω≫1ω≫1, JvJv is the Bessel function of the first kind and of order vv, ff is a sufficiently smooth function on [0,1][0,1]. Firstly, we express the moments in a closed form with the aid of special functions. Secondly, we induce the Filon-type method based on the Taylor interpolation polynomial at two endpoints and the Hermite interpolation polynomial at Clenshaw–Curtis points on evaluating the highly oscillatory Bessel integrals with algebraic singularity. Theoretical results and numerical experiments perform that the methods are very efficient in obtaining very high precision approximations if ωω is sufficiently large.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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