An investigation of the stability of certain two-layer difference schemes

Abstract

Estimates of the stability of weighted difference schemes in the norms of Banach spaces are constructed. On the basis of these, corresponding estimates are obtained for the stability, in the norms of the spaces C_h and L_ph, 1 ⩽ p ∞, of difference schemes which approximate an initial-boundary value problem for the heat-conduction equation with boundary conditions of the first, second and third kinds.