On highly oscillatory problems arising in electronic engineering
Condon, Marissa and Deaño, Alfredo and Iserles, Arieh (2009) On highly oscillatory problems arising in electronic engineering. ESAIM Mathematical Modelling and Numerical Analysis, 43 (4). pp. 785-804. ISSN 0764-583X
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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.
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