Local Interpolation Splines and Solution of Integro-Differential Equations of Mechanic’s Problems

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Local Interpolation Splines and Solution of Integro-Differential Equations of Mechanic’s Problems. / Burova, I. G.

In: WSEAS Transactions on Applied and Theoretical Mechanics, Vol. 17, 28.07.2022, p. 103-112.

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

BibTeX

@article{62ce411337a5470db523299de1cd5081,

title = "Local Interpolation Splines and Solution of Integro-Differential Equations of Mechanic{\textquoteright}s Problems",

abstract = "-Integro-differential equations are encountered when solving various problems of mechanics. Although Integro-Differential equations are encountered frequently in mathematical analysis of mechanical problems, very few of these equations will ever give us analytic solutions in a closed form. So that construction of numerical methods is the only way to find the approximate solution. This paper discusses the calculation schemes for solving integro-differential equations using local polynomial spline approximations of the Lagrangian type of the fourth and fifth orders of approximation. The features of solving integro-differential equations with the first derivative and the Fredholm and Volterra integrals of the second kind are discussed. Using the proposed spline approximations, formulas for numerical differentiation are obtained. These formulas are used to approximate the first derivative of a function. The numerical experiments are presented.",

keywords = "Fredholm integro-differential equations, local polynomial splines, numerical solution, problems of mechanics, Volterra-Fredholm integro-differential equations",

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

year = "2022",

month = jul,

day = "28",

doi = "10.37394/232011.2022.17.14",

language = "English",

volume = "17",

pages = "103--112",

journal = "WSEAS Transactions on Applied and Theoretical Mechanics",

issn = "1991-8747",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Local Interpolation Splines and Solution of Integro-Differential Equations of Mechanic’s Problems

AU - Burova, I. G.

PY - 2022/7/28

Y1 - 2022/7/28

N2 - -Integro-differential equations are encountered when solving various problems of mechanics. Although Integro-Differential equations are encountered frequently in mathematical analysis of mechanical problems, very few of these equations will ever give us analytic solutions in a closed form. So that construction of numerical methods is the only way to find the approximate solution. This paper discusses the calculation schemes for solving integro-differential equations using local polynomial spline approximations of the Lagrangian type of the fourth and fifth orders of approximation. The features of solving integro-differential equations with the first derivative and the Fredholm and Volterra integrals of the second kind are discussed. Using the proposed spline approximations, formulas for numerical differentiation are obtained. These formulas are used to approximate the first derivative of a function. The numerical experiments are presented.

AB - -Integro-differential equations are encountered when solving various problems of mechanics. Although Integro-Differential equations are encountered frequently in mathematical analysis of mechanical problems, very few of these equations will ever give us analytic solutions in a closed form. So that construction of numerical methods is the only way to find the approximate solution. This paper discusses the calculation schemes for solving integro-differential equations using local polynomial spline approximations of the Lagrangian type of the fourth and fifth orders of approximation. The features of solving integro-differential equations with the first derivative and the Fredholm and Volterra integrals of the second kind are discussed. Using the proposed spline approximations, formulas for numerical differentiation are obtained. These formulas are used to approximate the first derivative of a function. The numerical experiments are presented.

KW - Fredholm integro-differential equations

KW - local polynomial splines

KW - numerical solution

KW - problems of mechanics

KW - Volterra-Fredholm integro-differential equations

UR - http://www.scopus.com/inward/record.url?scp=85135437361&partnerID=8YFLogxK

U2 - 10.37394/232011.2022.17.14

DO - 10.37394/232011.2022.17.14

M3 - Article

AN - SCOPUS:85135437361

VL - 17

SP - 103

EP - 112

JO - WSEAS Transactions on Applied and Theoretical Mechanics

JF - WSEAS Transactions on Applied and Theoretical Mechanics

SN - 1991-8747

ER -

ID: 97983441