CONSTRUCTION OF A REGULARIZATION OF THE SOLUTION FOR AN EQUATION VOLTERRA OF THE FIRST KIND

Abstract

The importance of this topic is related to the study of solutions to ill-posed problems, since many physical processes of the medium are described by such differential equations. Inverse problems are of great practical importance in such areas of science as: problems of interpretation by physical automatic control devices, inverse problems of gravimetry, kinematics and The paper investigates an ill-posed problem in the form of a Volterra integral equation of the first kind with two independent variables. Volterra integral equations are widely used in problems of astronomy, biology, ecology, electrodynamics and mechanics. At present, more and more new areas are emerging in which the main processes are modulated by integral equations of the first, second and third kind. The construction of a regularization algorithm using the methods of successive approximation and a small parameter takes place in this work. At the same time, the issues of the uniqueness of the solution, as well as the construction of regularizing families of operators and estimating their efficiency, come to the fore. The results of this work can be applied and used to prove regularizability in a generalized sense for applied problems. Thus, in this article there is an extended solution for constructing a regularization of an integral equation, finding a sufficient solution by applying the principle of contraction mappings and an auxiliary function.