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Applications of Steklov-type eigenvalue problems to convergence of difference schemes for parabolic and hyperbolic equations with dynamical boundary conditions

  • Lubin G. Vulkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1196)

Abstract

Parabolic and hyperbolic equations with dynamical boundary conditions, i.e which involve first and second order time derivatives respectively, are considered. Convergence and stability of weighted difference schemes for such problems are discussed. Norms arising from Steklov-type eigenvalues problems are used, while in previously investigations, norms corresponding to Neumann's or Robin's boundary conditions are used. More exact stability conditions are obtained for the difference schemes parameters.

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References

  1. 1.
    Samarskii, A. A.: Theory of difference schemes. Nauka, Moscow, 1977 (in Russian)Google Scholar
  2. 2.
    Samarskii, A. A., Goolin A. V.: Stability of difference schemes. Nauka, Moscow, 1973 (in Russian)Google Scholar
  3. 3.
    Goolin, A. V.: On the stability of symmetrizable difference schemes. Mathematical Modeling 6 (1994) 9–13Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Lubin G. Vulkov
    • 1
  1. 1.Center of Applied Mathematics and InformaticsUniversity of RousseRousseBulgaria

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