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December  2010, 28(4): 1345-1367. doi: 10.3934/dcds.2010.28.1345

On systems of differential equations with extrinsic oscillation

Marissa Condon 1, , Alfredo Deaño 2, and  Arieh Iserles 3,

1. 

School of Electronic Engineering, Dublin City University, Dublin 9, Ireland
2. 

Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid, Spain
3. 

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom

Received  October 2009 Revised  February 2010 Published  June 2010

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: Modulated Fourier series, Asymptotic expansions., Oscillatory problems, Ordinary differential equations.
Mathematics Subject Classification: Primary: 34E05, 34E10, 65T40; Secondary: 65L0.
Citation: Marissa Condon, Alfredo Deaño, Arieh Iserles. On systems of differential equations with extrinsic oscillation. Discrete & Continuous Dynamical Systems, 2010, 28 (4) : 1345-1367. doi: 10.3934/dcds.2010.28.1345
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