A stroboscopic averaging algorithm for highly oscillatory delay problems

Sanz Serna, Jesús María; Zhu, Beibei

A stroboscopic averaging algorithm for highly oscillatory delay problems

Author(s): Sanz Serna, Jesús María; Zhu, Beibei

Publisher: Oxford University Press

Issued date: 2019-07

Citation: Sanz-Serna, J. M. & Zhu, B. (2019). A stroboscopic averaging algorithm for highly oscillatory delay problems. IMA Journal of Numerical Analysis, 39(3), 1110–1133.

ISSN: 0272-4979

DOI: https://doi.org/10.1093/imanum/dry020

xmlui.dri2xhtml.METS-1.0.item-contributor-funder: Ministerio de Economía y Competitividad (España)

Sponsor: J.M. Sanz-Serna has been supported by projects MTM2013-46553-C3-1-P from Ministerio de Economía y Comercio, and MTM2016-77660-P(AEI/FEDER, UE) from Ministerio de Economía, Industria y Competitividad, Spain. Beibei Zhu has been supported by the National Natural Science Foundation of China (Grant No. 11371357 and No. 11771438). She is grateful to Universidad Carlos III de Madrid for hosting the stay in Spain that made this work possible and to the Chinese Scholarship Council for providing the necessary funds. The authors are thankful to M. A. F. Sanjuán and A. Daza for bringing to their attention the vibrational resonance phenomenon, the toggle switch problem and other highly-oscillatory systems with delay.

Project: Gobierno de España. MTM2013-46553-C3-1-P
Gobierno de España. MTM2016-77660-P

Keywords: Delay differential equations , Stroboscopic averaging , Highly oscillatory problems

URI: http://hdl.handle.net/10016/32524

Rights: © The Author(s) 2018. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.

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 O(H2+1/Ω2) errors [+]

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