Ukrainian Mathematical Journal

, Volume 49, Issue 6, pp 865–870 | Cite as

Construction of approximations for a stationary solution of a system of singular ordinary differential equations

  • I. M. Romanyshyn
  • L. A. Synyts’kyi
Article
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Abstract

We propose a procedure for the construction of successive approximations of a stationary solution of a system of nonlinear ordinary differential equations with a small parameter with the derivative. We present sufficient conditions for the convergence of constructed approximations to the required stationary solution.

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References

  1. 1.
    B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow, (1967).Google Scholar
  2. 2.
    A. B. Vasil’eva and V. F. Butuzov, Asymptotic Decompositions of Solutions of Singularly Perturbed Equations [in Russian], Nauka, Moscow (1973).Google Scholar
  3. 3.
    D. Greenspan, “A new explicit discrete mechanics with applications,” J. Franklin Inst., 294, No. 4 (1972).Google Scholar
  4. 4.
    G. E. Shilov, Mathematical Analysis (Functions of Several Variables) [in Russian], Vols. 1, 2, Nauka, Moscow (1972)Google Scholar
  5. 5.
    I. M. Romanishin and L. A. Sinitskii, “Analysis of systems with smooth changes in parameters of input influence,” Teor. Électrotekhnika, 51, 72–78 (1992).Google Scholar
  6. 6.
    Ya. I. Khurgin and V. P. Yakovlev, Finite Functions in Physics and Engineering [in Russian], Nauka, Moscow (1971).Google Scholar
  7. 7.
    A. B. Vasil’eva, “Asymptotic methods in the theory of ordinary differential equations with small parameters with higher derivatives,” Zh. Vychisl. Mat. Mat. Fiz., 3, No. 4, 611–643 (1963).MathSciNetGoogle Scholar
  8. 8.
    A. B. Vasil’eva and V. F. Butuzov, Asymptotic Methods in the Theory of Singular Perturbations [in Russian], Vyshcha Shkola, Moscow (1990).MATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • I. M. Romanyshyn
    • 1
  • L. A. Synyts’kyi
    • 2
  1. 1.Physicomechanical InstituteUkrainian Academy of SciencesLviv
  2. 2.Lviv UniversityLviv

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