On highly oscillatory problems arising in electronic engineering
School of Electronic Engineering, Dublin City University, Dublin 9, Ireland.
2 Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA, UK. A.Iserles@damtp.cam.ac.uk
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.
Mathematics Subject Classification: 65L05 / 65T99
Key words: High oscillation / quadrature / ordinary differential equations.
© EDP Sciences, SMAI, 2009