Efficient computation of delay differential equations with highly oscillatory terms

Condon, Marissa and Deaño, Alfredo and Iserles, Arieh and Kropielnicka, Karolina (2012) Efficient computation of delay differential equations with highly oscillatory terms. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 46 (6). pp. 1407-1420. ISSN 0764-583X. (doi:https://doi.org/10.1051/m2an/2012004) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Official URL
https://doi.org/10.1051/m2an/2012004

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
Uncontrolled keywords: Delay differential equations / asymptotic expansions / modulated Fourier expansions / numerical analysi
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 20 Nov 2018 18:07 UTC
Last Modified: 21 Nov 2018 10:32 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70216 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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