The Newton—Kantorovich method in the theory of autonomous Noetherian boundary-value problems in the case of parametric resonance

1Chuiko, SM
2Nesmelova, OV
1Donbass State Pedagogical University, Slovyansk
2Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Sloviansk
Dopov. Nac. akad. nauk Ukr. 2019, 12:3-12
https://doi.org/10.15407/dopovidi2019.12.003
Section: Mathematics
Language: Russian
Abstract: 

We have found constructive conditions of solvability and a convergent iterative scheme for constructive solutions of a nonlinear autonomous Noetherian boundary-value problem in the case of parametric resonance. As an example of applying the scheme, some approximations to the solution of a periodic boundary-value problem for an autonomous equation of the Duffing type with a parametric perturbation are determined. To control the accuracy of the approximations, residuals in the original equation are applied.

Keywords: case of parametric resonance, Duffing-type equation, nonlinear autonomous boundary-value problem
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