We determine necessary and sufficient conditions for the existence of solutions of a nonlinear boundaryvalue problem for a system of difference-algebraic equations in the case of parametric resonance. We construct a convergent iterative algorithm for finding approximations to the solutions of nonlinear boundaryvalue problem for the system of difference-algebraic equations in the case of parametric resonance. As an example of application of the constructed iterative scheme, we obtain approximations to the solutions of a two-point boundary-value problem for a system of Mathieu-type difference-algebraic equations with parametric perturbation. To check the accuracy of the obtained approximations to the solutions of the two-point boundary-value problem for the system of Mathieu-type difference-algebraic equations with parametric perturbation, we use the discrepancies in the original equation.
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Translated from Neliniini Kolyvannya, Vol. 24, No. 1, pp. 128–140, January–March, 2021.
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Chuiko, S.M., Chuiko, O.V. & Kalinichenko, Y.V. Nonlinear Difference-Algebraic Boundary-Value Problem in the Case of Parametric Resonance. J Math Sci 265, 703–717 (2022). https://doi.org/10.1007/s10958-022-06078-2
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DOI: https://doi.org/10.1007/s10958-022-06078-2