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On second-order differential equations with highly oscillatory forcing terms

Condon, Marissa and Deano, Alfredo and Iserles, Arieh (2010) On second-order differential equations with highly oscillatory forcing terms. Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences, 466 (2118). pp. 1809-1828. ISSN 1364-5021

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Abstract

We present a method to compute efficiently solutions of systems of ordinary differential equations 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 ODE solvers: rstly, the construction of the numerical solution is more efficient when the system is highly oscillatory, and secondly, the cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided, motivated by problems in electronic engineering.

Item Type:Article (Published)
Refereed:Yes
Uncontrolled Keywords:Highly oscillatory problems, Ordinary dierential equations, Modulated Fourier expansions, Numerical analysis 1.
Subjects:Mathematics > Differential equations
DCU Faculties and Centres:UNSPECIFIED
Publisher:The Royal Society Publishing
Official URL:http://10.1098/rspa.2009.0481
Copyright Information:© 2010 The Royal Society
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:16239
Deposited On:07 Mar 2011 10:44 by Miriam Corcoran. Last Modified 07 Mar 2011 10:47

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