On Highly Oscillatory Problems Arising in Electronic Engineering Articles uri icon

publication date

  • January 2009

start page

  • 785

end page

  • 804


  • 4


  • 43

International Standard Serial Number (ISSN)

  • 0764-583X

Electronic International Standard Serial Number (EISSN)

  • 1290-3841


  • 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.