ABSTRACT
This chapter considers the line method and that of finite differences problems. It explores convergence of the finite difference schemes under suitable conditions on the data of our problems and shows that sufficiently smooth solutions can be approximated by such schemes. It examines the smoothness of solutions as it depends on the smoothness of the data, and proves the existence of solutions that possess sufficient smoothness to be approximated by finite differences. The chapter considers the continuation problem for the nonstationary boundary layer and an implicit difference scheme for the same problem. It shows the finite difference method to construct a solution of the boundary layer system in the case of a non-stationary axially symmetric flow.
