On the convergence of the method of successive approximations for the solutions of boundary layer type equations
In the title method, the impulse and energy equations are integrated twice along the normed normal to body coordinate \(\eta\) taking into account boundary conditions: first from \(\eta\) to \(\eta=1\) (exterior boundary), and then from \(\eta=0\) (the body surface) to \(\eta\). To solve the arising system of integro-differential equations, one employs an iterative algorithm which uses at each iteration special control functions to satisfy exactly the boundary conditions on the body surface and on the exterior boundary. There are a lot of numerical experiments that confirm practical convergence of the method. Here, on a simple self-similar example for heat equation, the author establishes the convergence theoretically. (For an another situation where the convergence of the above iterative method was proved exactly, see the reviewer [Žurn. vyčislit. Mat. mat. Fiz. 19, No. 3, 701-707 (1979; Zbl 0405.76019)]).
system of integro-differential equations
scientific article; zbMATH DE number 1028465