On second-order differential equations with highly oscillatory forcing terms

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 essentially independent of the oscillatory parameter. Numerical examples are provided, featuring the Van der Pol and Duffing oscillators and motivated by problems in electronic engineering.A. Deaño acknowledges financial support from the Spanish Ministry of Education under the programme of postdoctoral grants (Programa de becas postdoctorales) and project MTM2006-09050. The material is based upon works supported by Science Foundation Ireland under Principal Investigator Grant No. 05/IN.1/I18.Publicad