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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


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On the convergence of difference schemes for the generalized BBM–Burgers equation

Givi Berikelashvili
  • Corresponding author
  • A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 6 Tamarashvili Str., 0177; and Department of Mathematics, Georgian Technical University, 77 Kostava Str., Tbilisi 0175, Georgia
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/ Manana Mirianashvili
  • Muskhelishvili Institute of Computational Mathematics of the Georgian Technical University, 4 Grigol Peradze Str., Tbilisi 0131, Georgia
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Published Online: 2018-11-14 | DOI: https://doi.org/10.1515/gmj-2018-0075

Abstract

A three-level finite difference scheme is studied for the initial-boundary value problem of the generalized Benjamin–Bona–Mahony–Burgers equation. The obtained algebraic equations are linear with respect to the values of the desired function for each new level. The unique solvability and absolute stability of the difference scheme are shown. It is proved that the scheme is convergent with the rate of order k-1 when the exact solution belongs to the Sobolev space W2k(Q), 1<k3.

Keywords: Generalized BBM–Burgers equation; difference scheme; absolutely stable; scale of convergence rate estimates; Sobolev space

MSC 2010: 65M06; 65M12; 76B15

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About the article

Received: 2016-10-12

Revised: 2016-12-25

Accepted: 2016-12-30

Published Online: 2018-11-14


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0075.

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