Geodesic
On constructing the generally periodical solutions of a complicated structure of a non-autonomous system of differential equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 63-70 
A. N. Pchelintsev. On constructing the generally periodical solutions of a complicated structure of a non-autonomous system of differential equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 63-70. http://geodesic.mathdoc.fr/item/SJVM_2013_16_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a numerical scheme of constructing approximate generally periodical solutions of a complicatedtructure of a non-autonomous system of ordinary differential equations with the periodical right-hand sides on the surface of a torus is considered. The existence of such solutions as well as convergence of the method of successive approximations are shown. There are given results of the computational experiment.

[1] Afanasev A. P., Dzyuba S. M., Ustoichivost po Puassonu v dinamicheskikh i nepreryvnykh periodicheskikh sistemakh, LKI, M., 2007

[2] Pchelintsev A. N., Chislennye metody i obobschenno-periodicheskie resheniya dinamicheskikh sistem, Lambert Academic Publishing, Saarbrücken, 2010

[3] Kozlov V. V., “K teorii integrirovaniya uravnenii negolonomnoi mekhaniki”, Negolonomnye dinamicheskie sistemy. Integriruemost, khaos, strannye attraktory, eds. Borisov A. V., Mamaev I. S., Izd-vo Instituta kompyuternykh issledovanii, Moskva–Izhevsk, 2002, 149–173 | MR

[4] Kozlov V. V., Metody kachestvennogo analiza v dinamike tverdogo tela, Regulyarnaya i khaoticheskaya dinamika, Izhevsk, 2000 | MR

[5] Titchmarsh E., Teoriya funktsii, Nauka, M., 1980 | MR | Zbl

[6] Bari N. K., Trigonometricheskie ryady, Fizmatlit, M., 1961 | MR

[7] Nemytskii V. V., Stepanov V. V., Kachestvennaya teoriya differentsialnykh uravnenii, Editorial URSS, M., 2004

[8] Kalitkin N. N., Chislennye metody, Nauka, M., 1978 | MR

[9] Bor G., Pochti periodicheskie funktsii, Editorial URSS, M., 2005

[10] Demidovich B. P., Maron I. A., Osnovy vychislitelnoi matematiki, Lan, SPb., 2006