A stroboscopic averaging algorithm for highly oscillatory delay problems. (13th April 2018)

• Record Type: Journal Article
• Authors: Sanz-Serna, J M; Zhu, Beibei
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 3(2019)
• Page Start: 1110
• Page End: 1133
• Publication Date: 2018-04-13
• Subjects: delay differential equations -- stroboscopic averaging -- highly oscillatory problems; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry020
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: We propose and analyse a heterogeneous multiscale method for the efficient integration of constant-delay differential equations subject to fast periodic forcing. The stroboscopic averaging method suggested here may provide approximations with $\mathscr{O}\big (H^{2}+1/\varOmega ^{2}\big )$ errors with a computational effort that grows like $H^{-1}$ (the inverse of the step size), uniformly in the forcing frequency $\varOmega $ .