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Efficient computation of delay differential equations with highly oscillatory terms.

Condon, Marissa (2012) Efficient computation of delay differential equations with highly oscillatory terms. ESAIM: Mathematical Modelling and Numerical Analysis, 46 (6). pp. 1407-1420. ISSN 0764-583X

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Abstract

This paper is concerned with the asymptotic expansion and numerical solution of systems of linear delay differential equations with highly oscillatory forcing terms. The computation of such problems using standard numerical methods is exceedingly slow and inefficient, indeed standard software is practically useless for this purpose. We propose an alternative, consisting of an asymptotic expansion of the solution, where each term can be derived either by recursion or by solving a non-oscillatory problem. This leads to methods which, counter-intuitively to those developed according to standard numerical reasoning, exhibit improved performance with growing frequency of oscillation.

Item Type:Article (Published)
Refereed:Yes
Uncontrolled Keywords:Delay differential equations; asymptotic expansions; modulated Fourier expansions; numerical analysis
Subjects:Mathematics
Engineering > Electronic engineering
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Engineering and Computing > School of Electronic Engineering
Publisher:EDP Sciences
Official URL:http://dx.doi.org/10.1051/m2an/2012004
Copyright Information:© EDP Sciences 2012
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:16912
Deposited On:20 Apr 2012 10:42 by Fran Callaghan. Last Modified 20 Apr 2012 10:42

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