Solution of system of the Fredholm integral equation of the first kind
Journal Title: Modern Innovations, Systems and Technologies - Year 2021, Vol 1, Issue 4
Abstract
The article is devoted to the study of a system of two inhomogeneous Fredholm integral equations of the first kind with two required functions depending on one variable. Integral equations describe the restoration of a blurred image, production costs, etc. Fredholm integral equations with one desired function have been considered in many works, but relatively few works have been devoted to systems of such equations. The questions of stability for the solution of systems and the construction of a regularizing system of equations were investigated, but the solution was not constructed in an explicit form. In this paper, the kernels depend on two variables. The case is considered: in the kernels and inhomogeneities, the variables are separated in the equations; these functions are decomposed on the basis of two functions on the interval of integration. Examples of basic functions are given. A condition is determined under which the system has a unique solution in the chosen basis, formulated as a theorem. The solution is found in the form of an expansion in this basis. To illustrate the results obtained, an example is considered
Authors and Affiliations
Vladimir Uskov
Keywords
Related Articles
- EP ID EP706140
- DOI https://doi.org/10.47813/2782-2818-2021-1-4-1-7
- Views 99
- Downloads 0
Research of the physical-mechanical properties of wool fibers by carrying out full-factorial experiment
The scientific article covers a full-factorial experiment that has been carried out in order to evaluate the quality indicators of wool fibers stored, sorted and washed at different times and conditions. In addition, reg...
The impact of a cashless electronic payment system on hyperinflation in Bangladesh
The increase of electronic payment methods, or payments that don't include the use of currency has transformed financial transactions. Non-cash transactions are convenient, simple, and fast, among other benefits. Further...
Exploring collaborative filtering through K-Nearest Neighbors and Non-Negative Matrix Factorization
Collaborative filtering (CF) algorithms have received a lot of interest in recommender systems due to their ability to give personalized recommendations by exploiting user-item interaction data. In this article, we explo...
Optimization of the method for determining the fatty acid composition of dairy products
Chromatographic analysis of fatty acid methyl esters is used to characterize the lipid fraction of food products and is an effective method for detecting adulteration and one of the most important applications in food an...
Intellectualization of information processing systems for monitoring complex objects and systems
Creating intelligent information processing systems for monitoring complex technical objects and systems is an important task today. This paper presents the principles and models for creating systems of this class. The d...