On the stability in W22 of schemes with a decomposed operator

Abstract

WE here investigate the stability of the solution of a three-layer difference scheme with a decomposed operator in the norm of W 2 2 with initial conditions and the right-hand side approximating with order O( τ 2 + h 2) the general two-dimensional heat-conduction equation. For this equation we have the Cauchy problem with coefficients which are periodic in the space variables, a right-hand side and initial data. From the a priori estimate obtained and the approximation uniform convergence follows, by virtue of the difference analog of the embedding theorem [1, 2] and the theorem of [3]. In this paper we use the results of [2] and [4]–[6], in which similar questions are studied.