On systems of differential equations with extrinsic oscillation

Pages: 1345 - 1367, Volume 28, Issue 4, December 2010

doi:10.3934/dcds.2010.28.1345       Abstract        Full Text (1259.7K)       Related Articles

Marissa Condon - School of Electronic Engineering, Dublin City University, Dublin 9, Ireland (email)
Alfredo Deaño - Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid, Spain (email)
Arieh Iserles - Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom (email)

Abstract: We present a numerical scheme for an efficient discretization of nonlinear systems of differential equations subject to highly oscillatory perturbations. This method is superior to standard ODE numerical solvers in the presence of high frequency forcing terms, and is based on asymptotic expansions of the solution in inverse powers of the oscillatory parameter $\omega$, featuring modulated Fourier series in the expansion coefficients. Analysis of numerical stability and numerical examples are included.

Keywords:  Ordinary differential equations, Modulated Fourier series, Oscillatory problems, Asymptotic expansions.
Mathematics Subject Classification:  Primary: 34E05, 34E10, 65T40; Secondary: 65L05.

Received: October 2009;      Revised: February 2010;      Published: June 2010.