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On highly oscillatory problems arisingin electronic engineering

Published online by Cambridge University Press:  08 July 2009

Marissa Condon ,
Alfredo Deaño  and
Arieh Iserles
Marissa Condon
Affiliation:
School of Electronic Engineering, Dublin City University, Dublin 9, Ireland.
Alfredo Deaño
Affiliation:
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
Arieh Iserles
Affiliation:
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
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Abstract

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.

Keywords

High oscillationquadratureordinary differential equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 4: Special issue on Numerical ODEs today , July 2009 , pp. 785 - 804
Copyright
© EDP Sciences, SMAI, 2009

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