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On second order differential equations with highly oscillatory forcing terms

Condon, Marissa, Deaño, Alfredo, Iserles, Arieh (2010) On second order differential equations with highly oscillatory forcing terms. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466 . pp. 1809-1828. ISSN 1364-5021. (doi:10.1098/rspa.2009.0481) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1098/rspa.2009.0481

Abstract

We present a method to compute efficiently solutions of systems of ordinary differential equations (ODEs) 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 numerical ODE solvers: first, the construction of the numerical solution is more efficient when the system is highly oscillatory, and, second, the cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided, featuring the Van der Pol and Duffing oscillators and motivated by problems in electronic engineering.

Item Type: Article
DOI/Identification number: 10.1098/rspa.2009.0481
Uncontrolled keywords: highly oscillatory problems; ordinary differential equations; modulated Fourier expansions; numerical analysis
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Alfredo Deano-Cabrera
Date Deposited: 20 Nov 2018 18:22 UTC
Last Modified: 30 May 2019 08:21 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/70220 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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