On highly oscillatory problems arising in electronic engineering

Marissa Condon, Alfredo Deaño, Arieh Iserles
2009 Mathematical Modelling and Numerical Analysis  
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
more » ... curacy regardless of the rate of oscillation. Mathematics Subject Classification. 65L05, 65T99.
doi:10.1051/m2an/2009024 fatcat:xsbgvuwf2ffmtgwhjvmymzsnpe