WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 19, 2020
On the Solution of Fredholm Integral Equations of the First Kind
Authors: ,
Abstract: As it is well known the problem of solving the Fredholm integral equation of the first kind belongs to the class of ill-posed problems. The Tikhonov regularization method is well known. This method is usually applied to an integral equation and a system of linear algebraic equations. The authors firstly propose to reduce the integral equation of the first kind to a system of linear algebraic equations. This system is usually extremely ill-posed. Therefore, it is necessary to carry out the Tikhonov regularization for the system of equations. In this paper, to form a system of linear algebraic equations, local polynomial and non-polynomial spline approximations of the second order of approximation are used. The results of numerical experiments are presented.
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Keywords: Fredholm integral equation of the first kind, polynomial spline, non-polynomial spline, Tikhonov regularization.
Pages: 699-708
DOI: 10.37394/23206.2020.19.76