On some regularization algorithms for solving integral equations

Abstract

The problem of approximate finding stable solutions of ill-posed integral equations with constant integration limits is investigated with the use of the projection-iteration regularizing schemes based on Tikhonov’s and Fridman’s methods. The suggested approach assumes a substitution of the regularized integral equation for some sequence of more simple finite-dimensional problems that approximate this equation on the set of shrinking grids. For each approximate problem, only several approximations to the solution are found with applying some iterative procedure and the last of them is taken for the initial approximation in the iterative process for the next approximate problem with the use of the piecewise linear function. The sequence of constructed approximate solutions' linear interpolants is defined as the sequence of approximations to the initial integral equation’s solution. A comparative analysis of computational algorithms using various regularization strategies is carried out, the practical convergence of these algorithms for solving concrete problems is demonstrated.