Discrete Approximations and Periodic Solutions of Differential Inclusions

We consider two numerical methods for solving a periodic boundary value problem for a system of differential inclusions, the Galerkin method and the polygon method. To the original problem, we assign a sequence of its discretizations. Conditions under which the existence of solutions of the periodic boundary value problem implies the solvability of its discrete versions are presented. The convergence of the sequence of approximate solutions is analyzed.