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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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УДК 517.9  Найдены конструктивные условия разрешимости и схема построения решений линейной нетеровой краевой задачи для матричного разностного уравнения. Предложена оригинальная схема регуляризации линейной нетеровой краевой задачи для линейной вырожденной системы разностных уравнений.