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This article is cited in 1 scientific paper (total in 1 paper)
MATHEMATICAL MODELING AND NUMERICAL SIMULATION
Periodic boudary-value problem for Hill's equation in the case of parametric resonance
S. M. Chujko, O. V. Starkova, P. V. Kulish Donbass State Pedagogical University, 19 G. Batuka street, Donetsk region, Slavyansk, 84116, Ukraine
Abstract:
Necessary and sufficient conditions for the existence of solutions of nonlinear nonautonomous periodic problem for Hill's equation in the case of parametric resonance. A characteristic feature of the task is the need of finding, as desired solution, and the corresponding eigenfunction, which ensures solvability of the periodic problem for Hill's equation in the case of parametric resonance. To construct solutions of the periodic problem for Hill's equation and the corresponding eigenfunction in the case of parametric resonance propose diterative scheme, based on the method of simple iterations with used list-square technics.
Keywords:
nonlinear nonautonomous periodic boudary-value problem, Hill’s equation, the case of parametricresonance, he method of simple iterations.
Received: 27.10.2013
Citation:
S. M. Chujko, O. V. Starkova, P. V. Kulish, “Periodic boudary-value problem for Hill's equation in the case of parametric resonance”, Computer Research and Modeling, 6:1 (2014), 27–43
Linking options:
https://www.mathnet.ru/eng/crm302 https://www.mathnet.ru/eng/crm/v6/i1/p27
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