Efficient computation of delay differential equations with highly oscillatory terms
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1407-1420.

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.

DOI : 10.1051/m2an/2012004
Classification : 34E05, 34E99, 42A99, 34K28
Mots-clés : Delay differential equations, asymptotic expansions, modulated Fourier expansions, numerical analysis
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     title = {Efficient computation of delay differential equations with highly oscillatory terms},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1407--1420},
     publisher = {EDP-Sciences},
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Condon, Marissa; Deaño, Alfredo; Iserles, Arieh; Kropielnicka, Karolina. Efficient computation of delay differential equations with highly oscillatory terms. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1407-1420. doi : 10.1051/m2an/2012004. http://archive.numdam.org/articles/10.1051/m2an/2012004/

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