The Newton—Kantorovich method in the theory of autonomous Noetherian boundary-value problems in the case of parametric resonance
DOI:
https://doi.org/10.15407/dopovidi2019.12.003Keywords:
case of parametric resonance, Duffing-type equation, nonlinear autonomous boundary-value problemAbstract
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.
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