文献类型：期刊文献

英文题名：Numerical approximations of highly oscillatory Hilbert transforms

作者：Chen, Ruyun[1];Yu, Di[1];Chen, Juan[1]

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

年份：2020

卷号：39

期号：3

外文期刊名：COMPUTATIONAL & APPLIED MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:000542230500002)、、EI(收录号：20224112888382)、Scopus(收录号：2-s2.0-85086339484)、WOS

基金：The work is supported by Natural Science Foundation of Guangdong Province, China (No. 2015A030313615).

语种：英文

外文关键词：Hilbert transform; Multiple integral; Oscillatory kernel; Singularity; Numerical approximation; Error order

外文摘要：In this paper, we are concerned with the numerical approximations of one-sided Hilbert transforms with oscillatory kernel by means of the multiple integrals. This type of Hilbert transform has two computing difficulties: singularity and oscillation. To avoid the singularity, we transfer the Hilbert transform to an individual oscillatory integral which can be analytically calculated and a non-singular integral which can be well evaluated by the multiple integrals. Numerical examples are provided to illustrate the advantages of the proposed methods.