# Efficient computation of delay differential equations with highly oscillatory terms

Marissa Condon; Alfredo Deaño; Arieh Iserles; Karolina Kropielnicka

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 6, page 1407-1420
- ISSN: 0764-583X

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topCondon, Marissa, et al. "Efficient computation of delay differential equations with highly oscillatory terms." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1407-1420. <http://eudml.org/doc/277850>.

@article{Condon2012,

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.},

author = {Condon, Marissa, Deaño, Alfredo, Iserles, Arieh, Kropielnicka, Karolina},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Delay differential equations; asymptotic expansions; modulated Fourier expansions; numerical analysis; delay differential equations; numerical examples; highly oscillatory forcing terms},

language = {eng},

month = {4},

number = {6},

pages = {1407-1420},

publisher = {EDP Sciences},

title = {Efficient computation of delay differential equations with highly oscillatory terms},

url = {http://eudml.org/doc/277850},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Condon, Marissa

AU - Deaño, Alfredo

AU - Iserles, Arieh

AU - Kropielnicka, Karolina

TI - Efficient computation of delay differential equations with highly oscillatory terms

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2012/4//

PB - EDP Sciences

VL - 46

IS - 6

SP - 1407

EP - 1420

AB - 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.

LA - eng

KW - Delay differential equations; asymptotic expansions; modulated Fourier expansions; numerical analysis; delay differential equations; numerical examples; highly oscillatory forcing terms

UR - http://eudml.org/doc/277850

ER -

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