Abstract
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
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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