Investigation on artificial boundary conditions constructed by periodization and introduction of a small parameter for subsonic flow problems

One way of numerical constructing of artificial boundary conditions (ABC) by means of difference potentials method is considered. This way was proposed by V. S. Ryaben'kii and S. V. Tsynkov for ABC construction in flow problems and had its base in a periodic auxiliary problem with a small parameter. An analysis and justification of this way on a model problem is suggested in this paper. The analysis is made in terms of a differential problem.