Fredholm Integral Equation and Splines of the Fifth Order of Approximation

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Fredholm Integral Equation and Splines of the Fifth Order of Approximation. / Burova, I. G.

In: WSEAS Transactions on Mathematics, Vol. 21, 20.05.2022, p. 260-270.

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

BibTeX

@article{eda149dd6ce8482fbbf6cb3123c324e6,

title = "Fredholm Integral Equation and Splines of the Fifth Order of Approximation",

abstract = "This paper considers the numerical solution of the Fredholm integral equation of the second kind using local polynomial splines of the fifth order of approximation and the fourth order of approximation (cubic splines). The basis splines in these cases occupy five and four adjacent grid intervals respectively. Different local spline approximations of the fifth (or fourth) order of approximation are used at the beginning of the integration interval, in the middle of the integration interval, and at the end of the integration interval. The construction of the calculation schemes for solving the Fredholm equation of the second kind with these splines is considered. The results of the numerical experiments on the approximation of functions and on the solution of the Fredholm integral equations are presented. The results of the solution of the integral equation which uses the polynomial splines of the fifth order of approximation are compared with ones obtained with cubic splines and with the application of the Simpson{\textquoteright}s method. Note that in order to achieve a given error using the approximation with quadratic splines, a denser grid of nodes is required than when using the approximation with the cubic splines or splines of the fifth order of approximation.",

keywords = "approximation, fifth order of approximation, fourth order of approximation, Fredholm integral equation of the second kind, polynomial local splines",

author = "Burova, {I. G.}",

year = "2022",

month = may,

day = "20",

doi = "10.37394/23206.2022.21.31",

language = "English",

volume = "21",

pages = "260--270",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Fredholm Integral Equation and Splines of the Fifth Order of Approximation

AU - Burova, I. G.

PY - 2022/5/20

Y1 - 2022/5/20

N2 - This paper considers the numerical solution of the Fredholm integral equation of the second kind using local polynomial splines of the fifth order of approximation and the fourth order of approximation (cubic splines). The basis splines in these cases occupy five and four adjacent grid intervals respectively. Different local spline approximations of the fifth (or fourth) order of approximation are used at the beginning of the integration interval, in the middle of the integration interval, and at the end of the integration interval. The construction of the calculation schemes for solving the Fredholm equation of the second kind with these splines is considered. The results of the numerical experiments on the approximation of functions and on the solution of the Fredholm integral equations are presented. The results of the solution of the integral equation which uses the polynomial splines of the fifth order of approximation are compared with ones obtained with cubic splines and with the application of the Simpson’s method. Note that in order to achieve a given error using the approximation with quadratic splines, a denser grid of nodes is required than when using the approximation with the cubic splines or splines of the fifth order of approximation.

AB - This paper considers the numerical solution of the Fredholm integral equation of the second kind using local polynomial splines of the fifth order of approximation and the fourth order of approximation (cubic splines). The basis splines in these cases occupy five and four adjacent grid intervals respectively. Different local spline approximations of the fifth (or fourth) order of approximation are used at the beginning of the integration interval, in the middle of the integration interval, and at the end of the integration interval. The construction of the calculation schemes for solving the Fredholm equation of the second kind with these splines is considered. The results of the numerical experiments on the approximation of functions and on the solution of the Fredholm integral equations are presented. The results of the solution of the integral equation which uses the polynomial splines of the fifth order of approximation are compared with ones obtained with cubic splines and with the application of the Simpson’s method. Note that in order to achieve a given error using the approximation with quadratic splines, a denser grid of nodes is required than when using the approximation with the cubic splines or splines of the fifth order of approximation.

KW - approximation

KW - fifth order of approximation

KW - fourth order of approximation

KW - Fredholm integral equation of the second kind

KW - polynomial local splines

UR - http://www.scopus.com/inward/record.url?scp=85133660972&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4ab870e9-ddfd-3ad9-b364-00c213f9d7d2/

U2 - 10.37394/23206.2022.21.31

DO - 10.37394/23206.2022.21.31

M3 - Article

AN - SCOPUS:85133660972

VL - 21

SP - 260

EP - 270

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 97348864