|1Chuiko, SM |
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|
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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