Application of Splines of the Seventh Order Approximation to the Solution of the Fredholm Integral Equations with Weekly Singularity

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Application of Splines of the Seventh Order Approximation to the Solution of the Fredholm Integral Equations with Weekly Singularity. / Бурова, Ирина Герасимовна ; Алцыбеев, Глеб Олегович.

In: WSEAS Transactions on Mathematics, Vol. 22, 53, 28.06.2023, p. 475-482.

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

BibTeX

@article{d1a9893517864e43b357ffe73574e3fb,

title = "Application of Splines of the Seventh Order Approximation to the Solution of the Fredholm Integral Equations with Weekly Singularity",

abstract = "We consider the construction of a numerical solution to the Fredholm integral equation of the second kind with weekly singularity using polynomial spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. In the beginning, in the middle, and at the end of the integration interval, we apply various modifications of the basis splines of the seventh order of approximation. We use the Gaussian-type quadrature formulas to calculate the integrals with a weakly singularity. 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 to solve integral equations are given.",

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

year = "2023",

month = jun,

day = "28",

doi = "10.37394/23206.2023.22.53",

language = "English",

volume = "22",

pages = "475--482",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Application of Splines of the Seventh Order Approximation to the Solution of the Fredholm Integral Equations with Weekly Singularity

AU - Бурова, Ирина Герасимовна

AU - Алцыбеев, Глеб Олегович

PY - 2023/6/28

Y1 - 2023/6/28

N2 - We consider the construction of a numerical solution to the Fredholm integral equation of the second kind with weekly singularity using polynomial spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. In the beginning, in the middle, and at the end of the integration interval, we apply various modifications of the basis splines of the seventh order of approximation. We use the Gaussian-type quadrature formulas to calculate the integrals with a weakly singularity. 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 to solve integral equations are given.

AB - We consider the construction of a numerical solution to the Fredholm integral equation of the second kind with weekly singularity using polynomial spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. In the beginning, in the middle, and at the end of the integration interval, we apply various modifications of the basis splines of the seventh order of approximation. We use the Gaussian-type quadrature formulas to calculate the integrals with a weakly singularity. 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 to solve integral equations are given.

UR - https://www.mendeley.com/catalogue/999c1994-d510-35e2-80c5-6f9aaccb9d2a/

U2 - 10.37394/23206.2023.22.53

DO - 10.37394/23206.2023.22.53

M3 - Article

VL - 22

SP - 475

EP - 482

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

M1 - 53

ER -

ID: 106809975