On the solution of fredholm integral equations of the first kind

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On the solution of fredholm integral equations of the first kind. / Burova, I. G.; Ryabov, V. M.

In: WSEAS Transactions on Mathematics, Vol. 19, 2020, p. 699-708.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{6aeb6603b9b8417a8925a3e0c4ada097,

title = "On the solution of fredholm integral equations of the first kind",

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.",

keywords = "Fredholm integral equation of the first kind, Non-polynomial spline, Polynomial spline, Tikhonov regularization",

author = "Burova, {I. G.} and Ryabov, {V. M.}",

year = "2020",

doi = "10.37394/23206.2020.19.76",

language = "English",

volume = "19",

pages = "699--708",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - On the solution of fredholm integral equations of the first kind

AU - Burova, I. G.

AU - Ryabov, V. M.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Fredholm integral equation of the first kind

KW - Non-polynomial spline

KW - Polynomial spline

KW - Tikhonov regularization

UR - http://www.scopus.com/inward/record.url?scp=85102721011&partnerID=8YFLogxK

U2 - 10.37394/23206.2020.19.76

DO - 10.37394/23206.2020.19.76

M3 - Article

AN - SCOPUS:85102721011

VL - 19

SP - 699

EP - 708

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 75325440