On effective methods of regularization with discretization of integral equations

In this paper, we review new works on approximate methods for solving the first kind of Fredholm integral equations. The projection method of Galerkin-Bubnov with Legendre wavelets is used for the numerical solution of the first kind of Fredholm integral equations. Numerical calculations and the pro...

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Bibliographic Details
Main Authors: Temirbekov, Nurlan M., Temirbekova, Laura N., Nurmangaliyeva, Maya B.
Format: Conference Proceeding
Language:English
Subjects:
Basis functions
Fredholm equations
Galerkin method
Integral equations
Linear algebra
Mathematical analysis
Regularization
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Summary:In this paper, we review new works on approximate methods for solving the first kind of Fredholm integral equations. The projection method of Galerkin-Bubnov with Legendre wavelets is used for the numerical solution of the first kind of Fredholm integral equations. Numerical calculations and the proven theorem show a very strong sensitivity of the solution to the accuracy of calculating double integrals for determining the elements of the matrix and the right-hand side of the system of linear algebraic equations, which are determined by cubature formulas or analytical formulas. Also, in this article we describe how to obtain a priori estimates and convergence of projection methods with bases in the form of wavelets on the half-intervals. The performed comparative analysis shows that the Galerkin method with basis functions in the form of Legendre wavelets is efficient in terms of accuracy and easy to implement.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0144856