STABILITY AND CONVERGENCE OF 2-LEVEL DIFFERENCE-SCHEMES IN INTEGRAL WITH RESPECT TO TIME NORMS

Nowadays the general theory of operator-difference schemes with operat ors acting in Hilbert spaces has been created for investigating the st ability of the difference schemes that approximate linear problems of mathematical physics. In most cases a priori estimates which are unifo rm with respect to the t norms are usually considered. In the investig ation of accuracy for evolutionary problems, special attention should be given to estimation of the difference solution in grid analogs of i ntegral with respect to the time norms. In this paper a priori estimat es in such norms have been obtained for two-level operator-difference schemes. Use of that estimates is illustrated by convergence investiga tion for schemes with weights for parabolic equation with the solution belonging to W-2(2,1) (Q(T)).