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Cybernetics and Systems Analysis

, Volume 46, Issue 2, pp 252–263 | Cite as

Construction and analysis of a nonlinear differential model for two-phase media

  • V. V. Skopetsky
  • O. A. Marchenko
  • T. A. Samoilenko
Article

An initial–boundary-value problem for a nonlinear system of one moisture-transfer or filtration parabolic equation and two hyperbolic equations from the theory of elasticity is analyzed. The rate of convergence is estimated for a time-continuous and completely discrete approximate solutions of the corresponding generalized problem set up by the Galerkin method.

Keywords

nonlinear system generalized solution finite-element method estimate of an approximate generalized solution estimate of a time-discrete approximate generalized solution 

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References

  1. 1.
    V. S. Deineka, I. V. Sergienko, and V. V. Skopetsky, Models and Methods to Solve Problems with Interface Conditions [in Russian], Naukova Dumka, Kyiv (1998).Google Scholar
  2. 2.
    V. S. Deineka and I. V. Sergienko, Models and Methods to Solve Problems in Inhomogeneous Media [in Russian], Naukova Dumka, Kyiv (2001).Google Scholar
  3. 3.
    V. V. Skopetsky, O. A. Marchenko, and T. A. Samoilenko, “Deriving a discrete approximate solution for a nonlinear dynamic system of two-phase soil media,” Cybern. Syst. Analysis, 45, No. 4, 562–574 (2009).CrossRefGoogle Scholar
  4. 4.
    M. F. Wheeler, “A priori L 2 error estimates for Galerkin approximations to parabolic partial differential equations,” SIAM J. Numer. Anal., 10, No. 4, 723–759 (1973).CrossRefMathSciNetGoogle Scholar
  5. 5.
    V. V. Skopetsky, O. A. Marchenko, and T. A. Samoilenko, “Approximate solution for a nonlinear differential model of filter soils,” Komp. Matematika, No. 1, 49–59 (2009).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • V. V. Skopetsky
    • 1
  • O. A. Marchenko
    • 1
  • T. A. Samoilenko
    • 1
  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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