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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

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

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Volume 18, Issue 4


A one-parameter family of difference schemes for the regularized long-wave equation

Givi Berikelashvili
  • A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2 University Str., Tbilisi 0186; and Department of Mathematics, Georgian Technical University, 77 M. Kostava Str., Tbilisi 0175, Georgia.
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/ Manana Mirianashvili
  • N. Muskhelishvili Institute of Computational Mathematics, 8 Akuri Str., Tbilisi 0171, Georgia.
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We consider an initial boundary-value problem for the regularized long-wave equation. A three level one-parameter family of conservative difference schemes is studied. Two level schemes are used to find the values of the unknown functions on the first level. A numerical method for selection of artificial boundary conditions is proposed. It is proved that the finite difference scheme converges at rate O(2 h2) when an exact solution belongs to the Sobolev space .

Keywords.: Finite difference scheme; convergence rate; regularized long-wave equation; artificial boundary conditions; solitary wave collisions; mass transfer; numerical results

About the article

Received: 2010-12-17

Published in Print: 2011-12-01

Citation Information: Georgian Mathematical Journal, Volume 18, Issue 4, Pages 639–667, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/GMJ.2011.0044.

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