文献类型：期刊文献

英文题名：On computation of finite-part integrals of highly oscillatory functions

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：460

外文期刊名：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:001369867000001)、、EI(收录号：20244817442590)、Scopus(收录号：2-s2.0-85210127928)、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：Oscillatory function; Finite-part integral; Hypersingular; Ordinary differential equation; Efficient computation

外文摘要：In this paper, we propose some methods to compute finite-part integral involving hypersingular and highly oscillatory factors. We first write the integral as the Cauchy principle value integral which is computed based on the variable upper limit integral and frequency parameterization. For computing the nonsingular integral, we use the integration by parts and interpolation. On this basis, we get an asymptotic method and a Filon-type method. In order to test the efficiency of the proposed methods and verify the correctness of the proposed theories, some numerical experiments are performed.