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The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations. / Burova, I.G.; Alcybeev, G.O.

In: WSEAS Transactions on Mathematics, Vol. 22, 25.05.2023, p. 409-418.

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

Harvard

Burova, IG & Alcybeev, GO 2023, 'The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations', WSEAS Transactions on Mathematics, vol. 22, pp. 409-418. https://doi.org/10.37394/23206.2023.22.48

APA

Burova, I. G., & Alcybeev, G. O. (2023). The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations. WSEAS Transactions on Mathematics, 22, 409-418. https://doi.org/10.37394/23206.2023.22.48

Vancouver

Burova IG, Alcybeev GO. The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations. WSEAS Transactions on Mathematics. 2023 May 25;22:409-418. https://doi.org/10.37394/23206.2023.22.48

Author

Burova, I.G. ; Alcybeev, G.O. / The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations. In: WSEAS Transactions on Mathematics. 2023 ; Vol. 22. pp. 409-418.

BibTeX

@article{c3896fd6c81c4c4b93851823c0d3b6c9,
title = "The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations",
abstract = "There are various numerical methods for solving integral equations. Among the new numericalmethods, methods based on splines and spline wavelets should be noted. Local interpolation splines of a low order of approximation have proved themselves well in solving differential and integral equations. In this paper, we consider the construction of a numerical solution to the Fredholm integral equation of the second kind using spline approximations of the seventh order of approximation. The support of the basi s spline of the seventh order of approximation occupies seven grid intervals. We apply various modifications of the basis splines of the seventh order of approximation at the beginning, the middle, and at the end of the integration interval. It is assumed that the solution of the integral equation is sufficiently smooth. The advantages of using splines of the seventh order of approximation include the use of a small number of grid nodes to achieve the required error of approximation. Numerical examples of the application of spline approximations of the seventh order for solving integral equations are given. ",
keywords = "Fredholm integral equation of the second kind, splines of the seventh order of approximation",
author = "I.G. Burova and G.O. Alcybeev",
year = "2023",
month = may,
day = "25",
doi = "10.37394/23206.2023.22.48",
language = "English",
volume = "22",
pages = "409--418",
journal = "WSEAS Transactions on Mathematics",
issn = "1109-2769",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations

AU - Burova, I.G.

AU - Alcybeev, G.O.

PY - 2023/5/25

Y1 - 2023/5/25

N2 - There are various numerical methods for solving integral equations. Among the new numericalmethods, methods based on splines and spline wavelets should be noted. Local interpolation splines of a low order of approximation have proved themselves well in solving differential and integral equations. In this paper, we consider the construction of a numerical solution to the Fredholm integral equation of the second kind using spline approximations of the seventh order of approximation. The support of the basi s spline of the seventh order of approximation occupies seven grid intervals. We apply various modifications of the basis splines of the seventh order of approximation at the beginning, the middle, and at the end of the integration interval. It is assumed that the solution of the integral equation is sufficiently smooth. The advantages of using splines of the seventh order of approximation include the use of a small number of grid nodes to achieve the required error of approximation. Numerical examples of the application of spline approximations of the seventh order for solving integral equations are given.

AB - There are various numerical methods for solving integral equations. Among the new numericalmethods, methods based on splines and spline wavelets should be noted. Local interpolation splines of a low order of approximation have proved themselves well in solving differential and integral equations. In this paper, we consider the construction of a numerical solution to the Fredholm integral equation of the second kind using spline approximations of the seventh order of approximation. The support of the basi s spline of the seventh order of approximation occupies seven grid intervals. We apply various modifications of the basis splines of the seventh order of approximation at the beginning, the middle, and at the end of the integration interval. It is assumed that the solution of the integral equation is sufficiently smooth. The advantages of using splines of the seventh order of approximation include the use of a small number of grid nodes to achieve the required error of approximation. Numerical examples of the application of spline approximations of the seventh order for solving integral equations are given.

KW - Fredholm integral equation of the second kind

KW - splines of the seventh order of approximation

UR - https://www.mendeley.com/catalogue/4c65f666-dac7-3634-8080-01bf115f98a3/

U2 - 10.37394/23206.2023.22.48

DO - 10.37394/23206.2023.22.48

M3 - Article

VL - 22

SP - 409

EP - 418

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 105341965