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Inverse problem for the multidimensional elliptic equation with  Dirichlet-Neumann conditions is considered. High order of accuracy difference  schemes for the solution of inverse problem are presented. Stability, almost  coercive stability and coercive stability estimates of the third and fourth  orders of accuracy difference schemes for this problem are obtained.  Numerical results in a two dimensional case are given.

High order approximation of the inverse elliptic problem with Dirichlet-Neumann conditions