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On the convergence of difference schemes for generalized Benjamin–Bona–Mahony equation

Authors

  • Givi Berikelashvili,

    Corresponding author
    1. A. Razmadze Mathematical Institute of Tbilisi State University, Tbilisi, Georgia
    2. Department of Mathematics, Georgian Technical University, Tbilisi, Georgia
    • Correspondence to: G. Berikelashvili, A. Razmadze Mathematical Institute of Tbilisi State University, Tbilisi Georgia (e-mail: berikela@yahoo.com)

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  • Manana Mirianashvili

    1. N.Muskhelishvili Institute of Computational Mathematics, Tbilisi, Georgia
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Abstract

We consider an initial boundary-value problem for the generalized Benjamin–Bona–Mahony equation. A three-level conservative difference schemes are studied. The obtained algebraic equations are linear with respect to the values of unknown function for each new level. It is proved that the scheme is convergent with the convergence rate of order k – 1, when the exact solution belongs to the Sobolev space of order inline image. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 301–320, 2014

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