Efficient evaluation of oscillatory Bessel Hilbert transforms

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• 作者：Zhenhua Xu ; Shuhuang Xiang ; Guo He
• 关键词：65D32 ; 65D30
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2014
• 出版时间：1 March, 2014
• 年：2014
• 卷：258
• 期：Complete
• 页码：57-66
• 全文大小：531 K

文摘

In this paper, we study the asymptotics and evaluation of the oscillatory Bessel Hilbert transform with . The singularity of the Hilbert transform is transferred to an individual oscillatory integral independent of . 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.