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. 
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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/

[1] M. A. Krasnoselskii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, V. Ya. Stetsenko, Priblizhennye resheniya operatornykh uravnenii, M., 1969

[2] I. V. Skrypnik, Metody issledovaniya nelineinykh ellipticheskikh granichnykh zadach, M., 1990 | MR

[3] S. I. Pokhozhaev, “O razreshimosti nelineinykh uravnenii s nechetnymi operatorami”, Funkts. analiz i ego prilozh., 1:3 (1967), 66–73 | MR | Zbl

[4] F. E. Browder, “Nonlinear elliptic boundary problems and the generalized topological degree”, Bull. Amer. Math. Soc., 76:5 (1970), 999–1005 | DOI | MR | Zbl

[5] M. A. Krasnoselskii, P. P. Zabreiko, Geometricheskie metody nelineinogo analiza, M., 1975 | MR

[6] N. A. Bobylev, S. V. Emelyanov, S. K. Korovin, Geometricheskie metody v variatsionnykh zadachakh, M., 1998

[7] O. A. Ladyzhenskaya, Kraevye zadachi matematicheskoi fiziki, M., 1973 | MR

[8] V. S. Klimov, N. V. Senchakova, “Ob otnositelnom vraschenii mnogoznachnykh potentsialnykh vektornykh polei”, Matem. sb., 182:10 (1991), 1393–1407 | MR

[9] V. S. Klimov, “O topologicheskikh kharakteristikakh negladkikh funktsionalov”, Izv. RAN. Ser. mat., 62:5 (1998), 117–134 | MR | Zbl

[10] V. S. Klimov, “Periodicheskie resheniya parabolicheskikh vklyuchenii i metod usredneniya”, Dif. uravn., 46:12 (2010), 1722–1730 | Zbl