文献类型：期刊文献

英文题名：On quadrature of highly oscillatory Bessel function via asymptotic analysis of simplex integrals

作者：Zhou, Yongxiong[1];Chen, Ruyun[1]

机构：[1]Guangdong Ocean Univ, Fac Math & Comp Sci, Zhanjiang 524088, Peoples R China

年份：2025

卷号：456

外文期刊名：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:001307896100001)、、EI(收录号：20243616984979)、Scopus(收录号：2-s2.0-85202703095)、WOS

基金：The work is supported by Natural Science Foundation of Guangdong Province of China (No. 2022A1515010419) , and Educational Commission of Guangdong Province of China (No. 2020KTSCX049) .

语种：英文

外文关键词：Bessel function; Quadrature; Asymptotic expansion; Laplace transform

外文摘要：In this article, two methods for evaluating highly oscillatory Bessel integrals are explored. Firstly, a polynomial is analyzed as an effective approximation of the simplex integral of a highly oscillatory Bessel function based on Laplace transform, and its error rapidly decreases as the frequency increases. Furthermore, the inner product of f and highly oscillatory Bessel function can be approximated by two other forms of inner product by which one depends on a polynomial and the higher derivatives of f , another depends on Bessel function and the interpolation polynomial of f . In addition, three issues related to highly oscillatory Bessel integrals have also been discussed: inequalities for the convergence rate of Filontype methods, evaluation of Cauchy principal values, and simplified evaluation on infinite intervals. Through some preliminary numerical experiments, our theoretical analysis has been preliminarily confirmed, and the proposed numerical method is accurate and effective.