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On the convergence of difference schemes for generalized Benjamin–Bona–Mahony equation
Author(s) -
Berikelashvili Givi,
Mirianashvili Manana
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21810
Subject(s) - mathematics , sobolev space , convergence (economics) , partial differential equation , mathematical analysis , rate of convergence , partial derivative , order (exchange) , boundary value problem , space (punctuation) , algebraic equation , initial value problem , nonlinear system , channel (broadcasting) , linguistics , philosophy , physics , engineering , finance , quantum mechanics , electrical engineering , economics , economic growth
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 k , ( 1 < k ≤ 3 ) . © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 301–320, 2014