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

Givi Berikelashvili and Bidzina Midodashvili


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].

MSC: 65M06; 65M12

Funding source: Shota Rustaveli National Science Foundation

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

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

The authors thank an anonymous referee for valuable comments.


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Received: 2014-5-6
Revised: 2014-7-16
Accepted: 2014-8-2
Published Online: 2016-3-16
Published in Print: 2016-6-1

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