Asymptotic solvers for second-order differential equation systems with multiple frequencies Articles uri icon

publication date

  • March 2014

start page

  • 109

end page

  • 139


  • 1


  • 51

International Standard Serial Number (ISSN)

  • 0008-0624

Electronic International Standard Serial Number (EISSN)

  • 1126-5434


  • In this paper, an asymptotic expansion is constructed to solve second-order differential equation systems with highly oscillatory forcing terms involving multiple frequencies. An asymptotic expansion is derived in inverse of powers of the oscillatory parameter and its truncation results in a very effective method of dicretizing the differential equation system in question. Numerical experiments illustrate the effectiveness of the asymptotic method in contrast to the standard Runge-Kutta method. © 2013 Springer-Verlag Italia.


  • highly oscillatory problems; modulated fourier expansions; multiple frequencies; numerical analysis; second-order differential equations