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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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Volume 23, Issue 2


Method of corrections by higher order differences for elliptic equations with variable coefficients

Givi Berikelashvili
  • Corresponding author
  • A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 6 Tamarashvili Str., Tbilisi 0179; and Department of Mathematics, Georgian Technical University, 77 M. Kostava Str., Tbilisi 0175, Georgia
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/ Bidzina Midodashvili
  • Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, 13 University Str., Tbilisi 0186; and Faculty of Education, Exact and Natural Sciences, Gori Teaching University, 5 I. Chavchavadze Str., Gori, Georgia
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Published Online: 2016-03-16 | DOI: https://doi.org/10.1515/gmj-2016-0008


We consider the Dirichlet problem for an elliptic equation with variable coefficients, the solution of which is obtained by means of a finite-difference scheme of second order accuracy. We establish a two-stage finite-difference method for the posed problem and obtain an estimate of the convergence rate consistent with the smoothness of the solution. It is proved that the solution of the corrected scheme converges at rate O(|h|m) in the discrete L2-norm, when the solution of the original problem belongs to the Sobolev space with exponent m[2,4].

Keywords: Difference scheme; method of corrections; improvement of accuracy; compatible estimates of convergence rate

MSC: 65M06; 65M12


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About the article

Received: 2014-05-06

Revised: 2014-07-16

Accepted: 2014-08-02

Published Online: 2016-03-16

Published in Print: 2016-06-01

Funding Source: Shota Rustaveli National Science Foundation

Award identifier / Grant number: FR/406/5-106/12

The work was supported by the Shota Rustaveli National Science Foundation under the grant FR/406/5-106/12.

Citation Information: Georgian Mathematical Journal, Volume 23, Issue 2, Pages 169–180, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2016-0008.

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