Geodesic
About two finite-dimensional approximations of the periodic boundary value problem
Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 3, pp. 63-74

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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. 
@article{MAIS_2011_18_3_a6,
     author = {N. A. Dem'yankov},
     title = {About two finite-dimensional approximations of the periodic boundary value problem},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {63--74},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2011_18_3_a6/}
}
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N. A. Dem'yankov. About two finite-dimensional approximations of the periodic boundary value problem. Modelirovanie i analiz informacionnyh sistem, Tome 18 (2011) no. 3, pp. 63-74. http://geodesic.mathdoc.fr/item/MAIS_2011_18_3_a6/