Splines of the fourth order approximation and the Volterra integral equations

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Splines of the fourth order approximation and the Volterra integral equations. / Burova, I. G.; Doronina, A. G.; Zhilin, D. E.

In: WSEAS Transactions on Mathematics, Vol. 20, 2021, p. 475-488.

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

BibTeX

@article{c2afbffe04b44a02ad64e29ffb557f7c,

title = "Splines of the fourth order approximation and the Volterra integral equations",

abstract = "This paper is a continuation of a series of papers devoted to the numerical solution of integral equations using local interpolation splines. The main focus is given to the use of splines of the fourth order of approximation. The features of the application of the polynomial and non-polynomial splines of the fourth order of approximation to the solution of Volterra integral equation of the second kind are discussed. In addition to local splines of the Lagrangian type, integro-differential splines are also used to construct computational schemes. The comparison of the solutions obtained by different methods is carried out. The results of the numerical experiments are presented.",

keywords = "Non-polynomial spline, Polynomial spline, Volterra integral equation",

author = "Burova, {I. G.} and Doronina, {A. G.} and Zhilin, {D. E.}",

year = "2021",

doi = "10.37394/23206.2021.20.50",

language = "English",

volume = "20",

pages = "475--488",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Splines of the fourth order approximation and the Volterra integral equations

AU - Burova, I. G.

AU - Doronina, A. G.

AU - Zhilin, D. E.

PY - 2021

Y1 - 2021

N2 - This paper is a continuation of a series of papers devoted to the numerical solution of integral equations using local interpolation splines. The main focus is given to the use of splines of the fourth order of approximation. The features of the application of the polynomial and non-polynomial splines of the fourth order of approximation to the solution of Volterra integral equation of the second kind are discussed. In addition to local splines of the Lagrangian type, integro-differential splines are also used to construct computational schemes. The comparison of the solutions obtained by different methods is carried out. The results of the numerical experiments are presented.

AB - This paper is a continuation of a series of papers devoted to the numerical solution of integral equations using local interpolation splines. The main focus is given to the use of splines of the fourth order of approximation. The features of the application of the polynomial and non-polynomial splines of the fourth order of approximation to the solution of Volterra integral equation of the second kind are discussed. In addition to local splines of the Lagrangian type, integro-differential splines are also used to construct computational schemes. The comparison of the solutions obtained by different methods is carried out. The results of the numerical experiments are presented.

KW - Non-polynomial spline

KW - Polynomial spline

KW - Volterra integral equation

UR - http://www.scopus.com/inward/record.url?scp=85118672050&partnerID=8YFLogxK

U2 - 10.37394/23206.2021.20.50

DO - 10.37394/23206.2021.20.50

M3 - Article

AN - SCOPUS:85118672050

VL - 20

SP - 475

EP - 488

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 88342303