  A boundary value problem for a fractional power of the second-order elliptic
operator is considered. It is solved numerically using a time-dependent problem
for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard
two-level schemes with weights are applied. Stability conditions are obtained
for the fully discrete schemes under the consideration. The numerical results
are presented for a model two-dimensional boundary value problem wit a
fractional power of an elliptic operator. The dependence of accuracy on grids
in time and in space is studied.
