Weakly Nonlinear Matrix Boundary-Value Problem in the Case of Parametric Resonance
- Authors: Chuiko S.M.1, Chuiko A.S.1, Sysoev D.V.1
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Affiliations:
- Donbass State Pedagogic University
- Issue: Vol 223, No 3 (2017)
- Pages: 337-350
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239367
- DOI: https://doi.org/10.1007/s10958-017-3359-7
- ID: 239367
Cite item
Abstract
We establish necessary and sufficient conditions for the existence of solutions of a nonlinear matrix boundary-value problem for a system of ordinary differential equations in the case of parametric resonance. We construct a convergent iterative scheme for finding approximate solutions of the problem. As an example of application of the proposed iterative scheme, we obtain approximations to the solutions of a periodic boundary-value problem for the Riccati-type equation with parametric perturbation. To check the accuracy of the obtained approximations, we introduce residuals in the original equation.
About the authors
S. M. Chuiko
Donbass State Pedagogic University
Email: Jade.Santos@springer.com
Ukraine, General Batyuk Str., 19, Slavyansk, Donetsk Region, 84116
A. S. Chuiko
Donbass State Pedagogic University
Email: Jade.Santos@springer.com
Ukraine, General Batyuk Str., 19, Slavyansk, Donetsk Region, 84116
D. V. Sysoev
Donbass State Pedagogic University
Email: Jade.Santos@springer.com
Ukraine, General Batyuk Str., 19, Slavyansk, Donetsk Region, 84116