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Asymptotic expansions of periodic solutions of ordinary differential equations with large high-frequency terms

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Abstract

We consider the problem on the periodic solutions of a system of ordinary differential equations of arbitrary order n containing terms oscillating at a frequency ω ≫ 1 with coefficients of the order of ω n/2. For this problem, we construct the averaged (limit) problem and justify the averaging method as well as another efficient algorithm for constructing the complete asymptotics of the solution.

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References

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Authors and Affiliations

  1. Rostov State University, Rostov, Russia

    V. B. Levenshtam

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  1. V. B. Levenshtam
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Original Russian Text © V.B. Levenshtam, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 1, pp. 52–68.

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Levenshtam, V.B. Asymptotic expansions of periodic solutions of ordinary differential equations with large high-frequency terms. Diff Equat 44, 54–70 (2008). https://doi.org/10.1134/S0012266108010059

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  • DOI: https://doi.org/10.1134/S0012266108010059

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