Splines of the Second and Seventh Order Approximation and the Stability of the Solution of the Fredholm Integral Equations of the Second Kind"

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Splines of the Second and Seventh Order Approximation and the Stability of the Solution of the Fredholm Integral Equations of the Second Kind". / Бурова, Ирина Герасимовна ; Алцыбеев, Глеб Олегович ; Щипцова, Софья Андреевна.

In: WSEAS Transactions on Mathematics, Vol. 23, 2024, p. 1-15.

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

BibTeX

@article{c2fbc4f6269d4e0e840fad1ee0930cde,

title = "Splines of the Second and Seventh Order Approximation and the Stability of the Solution of the Fredholm Integral Equations of the Second Kind{"}",

abstract = "This work is a continuation of a series of works on the use of continuous local polynomial splines for solving interpolation problems and for solving the Fredholm integral equation of the second kind. Here the construction of a numerical solution to the Fredholm integral equation of the second kind using local spline approximations of the second order and the seventh order of approximation is considered. This paper is devoted to the investigation of the stability of the solution of the integral equation using these local splines. Approximation constants are given in the theorem about the error of approximation by the considered splines. Numerical examples of the application of spline approximations of the second and seventh order of approximation for solving integral equations are given.",

keywords = "Fredholm integral equation of the second kind, numerical solution, splines of the second order of approximation, splines of the seventh order of approximation, stability",

author = "Бурова, {Ирина Герасимовна} and Алцыбеев, {Глеб Олегович} and Щипцова, {Софья Андреевна}",

year = "2024",

doi = "10.37394/23206.2024.23.1",

language = "English",

volume = "23",

pages = "1--15",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Splines of the Second and Seventh Order Approximation and the Stability of the Solution of the Fredholm Integral Equations of the Second Kind"

AU - Бурова, Ирина Герасимовна

AU - Алцыбеев, Глеб Олегович

AU - Щипцова, Софья Андреевна

PY - 2024

Y1 - 2024

N2 - This work is a continuation of a series of works on the use of continuous local polynomial splines for solving interpolation problems and for solving the Fredholm integral equation of the second kind. Here the construction of a numerical solution to the Fredholm integral equation of the second kind using local spline approximations of the second order and the seventh order of approximation is considered. This paper is devoted to the investigation of the stability of the solution of the integral equation using these local splines. Approximation constants are given in the theorem about the error of approximation by the considered splines. Numerical examples of the application of spline approximations of the second and seventh order of approximation for solving integral equations are given.

AB - This work is a continuation of a series of works on the use of continuous local polynomial splines for solving interpolation problems and for solving the Fredholm integral equation of the second kind. Here the construction of a numerical solution to the Fredholm integral equation of the second kind using local spline approximations of the second order and the seventh order of approximation is considered. This paper is devoted to the investigation of the stability of the solution of the integral equation using these local splines. Approximation constants are given in the theorem about the error of approximation by the considered splines. Numerical examples of the application of spline approximations of the second and seventh order of approximation for solving integral equations are given.

KW - Fredholm integral equation of the second kind

KW - numerical solution

KW - splines of the second order of approximation

KW - splines of the seventh order of approximation

KW - stability

UR - https://wseas.com/journals/articles.php?id=8602

UR - https://www.mendeley.com/catalogue/2447c291-3416-3bc3-9fed-e719c0eb7704/

U2 - 10.37394/23206.2024.23.1

DO - 10.37394/23206.2024.23.1

M3 - Article

VL - 23

SP - 1

EP - 15

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 114370902