On highly oscillatory problems arising in electronic engineering
ESAIM: Modélisation mathématique et analyse numérique, Special issue on Numerical ODEs today, Tome 43 (2009) no. 4, pp. 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 : 10.1051/m2an/2009024
Classification : 65L05, 65T99
Mots-clés : high oscillation, quadrature, ordinary differential equations 
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     title = {On highly oscillatory problems arising in electronic engineering},
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Condon, Marissa; Deaño, Alfredo; Iserles, Arieh. On highly oscillatory problems arising in electronic engineering. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Numerical ODEs today, 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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