On the convergence of difference schemes for generalized Benjamin–Bona–Mahony equation |
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| Authors: | Givi Berikelashvili Manana Mirianashvili |
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| Affiliation: | 1. A. Razmadze Mathematical Institute of Tbilisi State University, , Tbilisi, Georgia;2. Department of Mathematics, Georgian Technical University, , Tbilisi, Georgia;3. 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  . © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 301–320, 2014 |
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| Keywords: | compatible estimate of convergence difference scheme generalized Benjamin– Bona– Mahony equation orbital stability |
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