Asymptotics and numerical approximation of highly oscillatory Hilbert transforms
作者：
Highlights：
• To the best of our knowledge, there is no research that aims at the asymptotic behaviour and numerical computation of highly oscillatory Hilbert transforms studied in this paper, which plays an important role in study of electromagnetic scattering problem.
• The asymptotic behaviour about ω was presented by transforming the Hilbert transforms into the integrals on [0,+∞) with the integrands that don’t oscillate and decay exponentially.
• We presented uniformly convergent numerical methods according to the position of singular point τ, by using Chebyshev approximation, Gauss Laguerre quadrature rule and Meijer G-function.
摘要
•To the best of our knowledge, there is no research that aims at the asymptotic behaviour and numerical computation of highly oscillatory Hilbert transforms studied in this paper, which plays an important role in study of electromagnetic scattering problem.•The asymptotic behaviour about ω was presented by transforming the Hilbert transforms into the integrals on [0,+∞) with the integrands that don’t oscillate and decay exponentially.•We presented uniformly convergent numerical methods according to the position of singular point τ, by using Chebyshev approximation, Gauss Laguerre quadrature rule and Meijer G-function.
论文关键词：Highly oscillatory Hilbert transforms,Meijer G–function,Chebyshev approximation,Gaussian quadrature rule
论文评审过程：Received 18 February 2020, Revised 9 June 2020, Accepted 5 July 2020, Available online 17 July 2020, Version of Record 17 July 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125525
