Strong stability of two-layer operator-difference schemes

The two-layer operator-difference schemes in the finite-dimensional Hilbert ;space are investigated. The estimates of strong stability with perturbed o perators (coefficient stability), perturbations of the right side and the i nitial data are obtained. The correspondent results are proved under natura l assumptions for perturbation of the operators. The investigation of the c oefficient stability is illustrated for the scheme with weights, approximat ing the initialboundary problem for the parabolic equation.