Nonstationary Collocation-Iterative Method for Constructing Approximate Solutions of Integro-Functional Equations with Small Nonlinearity

• Дата: 2026
• Автор: Геселева, Катерина
• Формат: Стаття
• Мова: Українська
• Опубліковано: Кам'янець-Подільський національний університет імені Івана Огієнка 2026
• Онлайн доступ: https://mcm-math.kpnu.edu.ua/article/view/360166
• Назва журналу: Mathematical and computer modelling. Series: Physical and mathematical sciences

Integro-functional equations occupy an important place in the mathematical modeling of a wide range of applied and interdisciplinary problems, particularly those related to dynamical systems with delay and deviating arguments. Such equations arise in the formulation of boundary-value and initial-value problems for differential equations with deviating arguments, including both delay and neutral types. In this case, the argument deviation may be either constant or variable. The presence of even small nonlinearity in such models significantly complicates the analysis of the existence, uniqueness, stability, and asymptotic behavior of their solutions, which necessitates the study and development of new approximate methods as well as the improvement of existing approaches for their investigation. One of the approaches to constructing approximate solutions of integro-functional equations is the projection-iterative method, a particular case of which is the collocation-iterative method. A significant advantage of the collocation-iterative method over the general projection-iterative scheme is the considerable simplification of the computational process, since at each iteration step, instead of calculating integrals of the residual, only its values at the collocation nodes are used. A particular and computationally simpler modification of this approach is the nonstationary collocation-iterative method. This paper investigates the application of the nonstationary collocation-iterative method to a class of integro-functional equations with small nonlinearity. Sufficient conditions for the convergence of this method are established. The obtained results can be applied to solving problems in applied mathematics, mechanics, control theory, and information technologies, where mathematical models are described by equations with deviating arguments.