In this paper, we consider an inverse elliptic problem with Neumann type
overdetermination and construct a fourth order of accuracy difference scheme
for its solution. Stability, almost coercive stability and coercive
stability estimates for the solution of difference problem are proved. Later,
we construct a fourth order difference scheme for an inverse problem for
multidimensional elliptic equation with Neumann type overdetermination and
Dirichlet boundary condition. Finally, we illustrate numerical example with
descriptions of numeric realization in a two-dimensional case.