Heseleva K. Collocation-Iterative Method for Solving Integro-Functional Equations

The thesis is devoted to the research of integro-functional equations concerning the existence of their solutions and methods of their finding. The importance of these equations is due in particular to the fact that such equations reduce boundary value problems for differential equations with a deviation of the argument of the neutral type, when the deviation of the argument can be a variable. Exact solutions of these equations can be found only in some cases, so it is important to study methods for constructing approximate solutions of these equations. One such method is the collocation-iterative method. The paper substantiates different variants of the collocation-iterative method (stationary and nonstationary) to solve integro-functional equations, both linear and with small nonlinearity. The conditions of convergence and estimation of the method error are established. Based on this, computational schemes are developed. The collocation-iterative method is applied to nonlinear integro-functional equations. The use of the method of successive approximations, the method of collocation and the collocation-iterative method to construct approximate solutions of a boundary value problem for a differential-functional equation is considered. Integra-functional equations with additional conditions are investigated. In this case, in addition to the question of applying the collocation-iterative method, there is a question of compatibility of the problem. The results of the dissertation have both theoretical and applied significance. They expand the scope of the collocation-iterative method and enrich the theory of integro-functional equations. Developed computational algorithms can be used to find solutions to specific mathematical models found in physics, biology, economics, medicine, and other fields of human activity. They can be used in further theoretical research on the application of the collocation-iterative method.