文献类型：期刊文献

英文题名：Numerical steepest descent method for computing oscillatory-type Bessel integral transforms☆

作者：Chen, Ruyun[1];Li, Yu[1];Zhou, Yongxiong[1]

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

年份：2025

卷号：236

起止页码：320

外文期刊名：MATHEMATICS AND COMPUTERS IN SIMULATION

收录：SCI-EXPANDED(收录号：WOS:001481146200001)、、EI(收录号：20251718306589)、Scopus(收录号：2-s2.0-105003376264)、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; Oscillatory integrals; Steepest descent method; Numerical integration

外文摘要：In this paper, numerical steepest descent method is implemented to approximate highly oscillatory Bessel-type integral transforms. We begin our analysis by utilizing an important relationship between Bessel function of the first kind and modified Bessel function of the second kind. Subsequently, we transform new integrals into the forms on the interval [0, +infinity), where the integrands do not oscillate and decay exponentially fast. These integrals can then be efficiently computed using Gauss-Laguerre quadrature rule. Furthermore, we derive the theoretical error estimates that depend on the frequency w and the number of nodes n. Numerical examples based on the theoretical results are provided to demonstrate the effectiveness of these methods.