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Once again on the Samoilenko numerical-analytic method of successive periodic approximations

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Abstract

A new numerical-analytic algorithm for the investigation of periodic solutions of nonlinear periodic systems of differential equations dx/dt = A(t) x+ ƒ(t, x) in the critical case is developed. The problem of the existence of solutions and their approximate construction is studied. Estimates for the convergence of successive periodic approximations are obtained.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 4, pp. 472–488, April, 2006.

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Korol’, I.I., Perestyuk, M.O. Once again on the Samoilenko numerical-analytic method of successive periodic approximations. Ukr Math J 58, 529–550 (2006). https://doi.org/10.1007/s11253-006-0083-8

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  • DOI: https://doi.org/10.1007/s11253-006-0083-8

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