On systems of differential equations with extrinsic oscillation

Marissa Condon; Alfredo Deaño; Arieh Iserles

doi:10.3934/dcds.2010.28.1345

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2010, Volume 28, Issue 4: 1345-1367. Doi: 10.3934/dcds.2010.28.1345

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On systems of differential equations with extrinsic oscillation

1.
School of Electronic Engineering, Dublin City University, Dublin 9
2.
Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid
3.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge

Received: October 2009

Revised: February 2010

Published: December 2010

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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.

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Mathematics Subject Classification: Primary: 34E05, 34E10, 65T40; Secondary: 65L05.

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