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.
Mots clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {785--804},
publisher = {EDP-Sciences},
volume = {43},
number = {4},
year = {2009},
doi = {10.1051/m2an/2009024},
mrnumber = {2542877},
zbl = {1172.78009},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2009024/}
}
TY - JOUR AU - Condon, Marissa AU - Deaño, Alfredo AU - Iserles, Arieh TI - On highly oscillatory problems arising in electronic engineering JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 785 EP - 804 VL - 43 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2009024/ DO - 10.1051/m2an/2009024 LA - en ID - M2AN_2009__43_4_785_0 ER -
%0 Journal Article %A Condon, Marissa %A Deaño, Alfredo %A Iserles, Arieh %T On highly oscillatory problems arising in electronic engineering %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 785-804 %V 43 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2009024/ %R 10.1051/m2an/2009024 %G en %F M2AN_2009__43_4_785_0
Condon, Marissa; Deaño, Alfredo; Iserles, Arieh. On highly oscillatory problems arising in electronic engineering. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 4, pp. 785-804. doi : 10.1051/m2an/2009024. http://www.numdam.org/articles/10.1051/m2an/2009024/
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