On Second-Order Differential Equations with Highly Oscillatory Forcing Terms Articles uri icon

publication date

  • January 2010

start page

  • 1809

end page

  • 1828


  • 2118


  • 466

International Standard Serial Number (ISSN)

  • 1364-5021

Electronic International Standard Serial Number (EISSN)

  • 1471-2946


  • We present a method to compute efficiently solutions of systems of ordinary differential equations (ODEs) that possess highly oscillatory forcing terms. This approach is based
    on asymptotic expansions in inverse powers of the oscillatory parameter,
    and features two fundamental advantages with
    respect to standard numerical ODE solvers: first, the construction of
    the numerical
    solution is more efficient when the system is
    highly oscillatory, and, second, the cost of the computation is
    independent of the oscillatory parameter. Numerical
    examples are provided, featuring the Van der Pol and Duffing
    and motivated by problems in electronic