Asymptotic analysis of some classes of ordinary differential equations with large high-frequency terms |
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Authors: | V. B. Levenshtam |
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Affiliation: | 1.Southern Federal University,Rostov-on-Don,Russia |
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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 ω n/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 ω d . 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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