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.
@article{M2AN_2012__46_6_1407_0,
author = {Condon, Marissa and Dea\~no, Alfredo and Iserles, Arieh and Kropielnicka, Karolina},
title = {Efficient computation of delay differential equations with highly oscillatory terms},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {46},
year = {2012},
pages = {1407-1420},
doi = {10.1051/m2an/2012004},
mrnumber = {2996333},
zbl = {1270.65032},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2012__46_6_1407_0}
}
Condon, Marissa; Deaño, Alfredo; Iserles, Arieh; Kropielnicka, Karolina. Efficient computation of delay differential equations with highly oscillatory terms. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) pp. 1407-1420. doi : 10.1051/m2an/2012004. http://gdmltest.u-ga.fr/item/M2AN_2012__46_6_1407_0/
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