The third boundary value problem for loaded differential Sobolev type equation and grid methods of their numerical implementation

摘要

In this paper, we consider the third boundary value problem for loaded differential Sobolev type equation and grid methods of their numerical implementation. To solve the problem, a priori estimates in differential and difference settings are obtained. These a priori estimates imply uniqueness and stability of the solution with respect to the initial data and the right-hand side on the layer, as well as the convergence of the solution of each of the difference problem to the solution of the corresponding differential problem.