Invariant difference schemes for parabolic equations with transformations of independent variables

In this paper, invariant difference schemes for nonstationary equations und er independent variables transformation constructed and investigated. Under invariance of difference scheme Ne mean its ability to preserve basic prop erties (stability, approximation, convergency, etc.) in various coordinate systems. Difference schemes of the second-order approximation that satisfy the invariance property are constructed for equations of parabolic type. St ability and convergency investigation of correspondent difference problems are carried out; a priori estimates in various grid norms are obtained.