A finite difference scheme for the approximation of the third initial boundary value parabolic problem

Abstract

We investigate the convergence of difference schemes that approximate the third initial boundary value problem for parabolic equations with time dependent coefficients. An abstract operator method is developed to analyze this equation. An estimate of the rate of the convergence in a special discrete $W_2^{1, 1/2}$ Sobolev norm, compatible with the smoothness of the solution is obtained.