Numerical solution of the first kind Fredholm integral equations by projection methods with wavelets as the basis functions

. In this paper, we review new works on approximate methods for solving the first kind Fredholm integral equations. The Galerkin-Bubnov projection method with Legendre wavelets is used for the numerical solution of the first kind 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 paper we obtain a priori estimates and convergence of the projection methods with bases in the form of wavelets on 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 is easy to implement.