Stability of weighted difference schemes

Estimates of stability of weighted differences in norms of Banach spaces are constructed. On the basis of these, corresponding estimates of stability in the norms of the spaces C_h and L_ph, 1 P < , are obtained for difference schemes which approximate an initial-boundary value problem for the heat equation with boundary conditions of the first, second, and third kinds. In addition, the estimates of resolvents of difference elliptic operators in C_h and L_ph, 1 P < , obtained in this article are used in an essential way.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 9, pp. 1254–1258, September, 1990.