Stability of two-layer operator-difference schemes with symmetric and skew-symmetric operators

Two-layer operator-difference schemes with weight parameters which contain symmetric and skew-symmetric operators are considered. Sufficient conditions and a priori estimates for stability are derived using the method of reduction to a three-layer operator-difference scheme. It is shown that the conditions are necessary ones for some particular cases. The results may be used for investigation of the grid problems approximating initial-boundary value problems of mathematical physics with convection transfer (of convection-diffusion type), including the problems with varying coefficients on various grids.