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On second-order differential equations with highly oscillatory forcing terms

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URI: https://hdl.handle.net/10016/6645
ISSN: 1364-5021 (Print)
ISSN: 1471-2946 (Online)
DOI: 10.1098/rspa.2009.0481
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2010
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The Royal Society
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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.
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Highly oscillatory problems, Ordinary differential equations, Modulated Fourier expansions, Numerical analysis
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Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, 2010, doi: 10.1098/rspa.2009.0481
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