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On systems of differential equations with extrinsic oscillation

Condon, Marissa and Deaño , Alfredo and Iserles, Arieh (2010) On systems of differential equations with extrinsic oscillation. Discrete and Continuous Dynamical Systems (DCDS-A), 28 (4). pp. 1345-1367. ISSN 1553-5231

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Abstract

We present a numerical scheme for an efficient discretization of nonlinear systems of differential equations subjected 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 w, featuring modulated Fourier series in the expansion coefficients. Analysis of numerical stability and numerical examples are included.

Item Type:Article (Published)
Refereed:Yes
Uncontrolled Keywords:Ordinary differential equations, Modulated Fourier series, Oscillatory problems, Asymptotic expansions.
Subjects:Mathematics > Differential equations
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Engineering and Computing > School of Electronic Engineering
Publisher:American Institute of Mathematical Sciences
Official URL:http://dx.doi.org/10.3934/dcds.2010.28.1345
Copyright Information:© American Institute of Mathematical Sciences 2010. This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems A following peer review. The definitive publisher-authenticated version Vol. 28(4) pp 1345-1367 is available online at: http://dx.doi.org/10.3934/dcds.2010.28.1345
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:16238
Deposited On:07 Mar 2011 10:29 by Miriam Corcoran. Last Modified 08 Aug 2014 12:00

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