About two finite-dimensional approximations of the periodic boundary value problem

N. A. Dem'yankov

P. G. Demidov Yaroslavl State University

Abstract: Two numerical methods for solving the periodic boundary value problem are considered: Galerkin's method and the method of polygonal lines. The original problem is mapped to the sequence of its discretization – systems of equations in finite spaces. Conditions under which the existence of solutions of a periodic boundary value problem entails its solvability of discrete options are given. The question of approximate solutions convergence is studied.

Keywords: numerical methods, boundary value problem, periodic solution, discrete version.

UDC: 519.6

Received: 01.03.2011