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Asymptotic analysis of some classes of ordinary differential equations with large high-frequency terms

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Abstract

A complete asymptotic expansion is constructed for solutions of the Cauchy problem for nth order linear ordinary differential equations with rapidly oscillating coefficients, some of which may be proportional to ωn/2, where ω is oscillation frequency. A similar problem is solved for a class of systems of n linear first-order ordinary differential equations with coefficients of the same type. Attention is also given to some classes of first-order nonlinear equations with rapidly oscillating terms proportional to powers ωd. For such equations with d ∈ (1/2, 1], conditions are found that allow for the construction (and strict justification) of the leading asymptotic term and, in some cases, a complete asymptotic expansion of the solution of the Cauchy problem.

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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, Russia

    V. B. Levenshtam

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  1. V. B. Levenshtam
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Correspondence to V. B. Levenshtam.

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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 27, Part I, pp. 144–177, 2009.

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Levenshtam, V.B. Asymptotic analysis of some classes of ordinary differential equations with large high-frequency terms. J Math Sci 163, 89–110 (2009). https://doi.org/10.1007/s10958-009-9660-3

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  • DOI: https://doi.org/10.1007/s10958-009-9660-3

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