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Highly oscillatory problems with time-dependent vanishing frequency

Chartier, Philippe
Lemou, Mohammed
Méhats, Florian
Published in SIAM Journal on Numerical Analysis. 2019, vol. 57, no. 2, p. 925-944
Abstract In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing for the possibility that the frequency actually depends on time and vanishes at some instants introduces additional difficulties from both the asymptotic analysis and numerical simulation points of view. This work is a first step towards the resolution of these difficulties. In particular, we show that it is still possible in this situation to infer the asymptotic behaviour of the solution at the price of more intricate computations and we derive a second order uniformly accurate numerical method.
Keywords Highly-oscillatory problemsTime-dependent vanishing frequencyAsymptotic expansionUniform accuracy
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Research group Analyse numérique
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CHARTIER, Philippe et al. Highly oscillatory problems with time-dependent vanishing frequency. In: SIAM Journal on Numerical Analysis, 2019, vol. 57, n° 2, p. 925-944. https://archive-ouverte.unige.ch/unige:118370

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Deposited on : 2019-05-28

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