On highly oscillatory problems arising in electronic engineering
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 4, p. 785-804

In this paper, we consider linear ordinary differential equations originating in electronic engineering, which exhibit exceedingly rapid oscillation. Moreover, the oscillation model is completely different from the familiar framework of asymptotic analysis of highly oscillatory integrals. Using a Bessel-function identity, we expand the oscillator into asymptotic series, and this allows us to extend Filon-type approach to this setting. The outcome is a time-stepping method that guarantees high accuracy regardless of the rate of oscillation.

DOI : https://doi.org/10.1051/m2an/2009024
Classification:  65L05,  65T99
Keywords: high oscillation, quadrature, ordinary differential equations
@article{M2AN_2009__43_4_785_0,
author = {Condon, Marissa and Dea\~no, Alfredo and Iserles, Arieh},
title = {On highly oscillatory problems arising in electronic engineering},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {43},
number = {4},
year = {2009},
pages = {785-804},
doi = {10.1051/m2an/2009024},
zbl = {1172.78009},
mrnumber = {2542877},
language = {en},
url = {http://www.numdam.org/item/M2AN_2009__43_4_785_0}
}

Condon, Marissa; Deaño, Alfredo; Iserles, Arieh. On highly oscillatory problems arising in electronic engineering. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 4, pp. 785-804. doi : 10.1051/m2an/2009024. http://www.numdam.org/item/M2AN_2009__43_4_785_0/

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