Ukrainian Mathematical Journal

, Volume 50, Issue 3, pp 484–488 | Cite as

An iteration method for the problem of averaging in the standard form

  • T. A. Mel’nik
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Abstract

An iteration method for the enhancement of the precision of an approximate solution of the problem of averaging in the standard form is considered.

Keywords

Approximate Solution Cauchy Problem Standard Form Small Parameter Naukova Dumka 

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References

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    N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).MATHGoogle Scholar
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    L. D. Akulenko, “Application of the methods of averaging and successive approximations for the investigation of nonlinear oscillations,” Prikl. Mat. Mekh., 45, Issue 5, 771–777 (1981).MathSciNetGoogle Scholar
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    A. N. Filatov, Asymptotic Methods in the Theory of Differential and Integro-Differential Equations [in Russian], Fan, Tashkent (1974).Google Scholar
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    A. M. Samoilenko, “The justification of the averaging principle for differential equations with discontinuous right-hand side,” in: Approximate Methods of Solution of Differential Equations [in Russian], Izd. Akad. Nauk Ukr. SSR, Kiev (1963), pp. 90–95.Google Scholar
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    N. N. Bogolyubov, Yu. A. Mitropol’skii, and A. M. Samoilenko, The Method of Fast Averaging in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev, (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • T. A. Mel’nik
    • 1
  1. 1.Odessa UniversityOdessa

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