Solution of Integral Equations Using Local Splines of the Second Order

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Solution of Integral Equations Using Local Splines of the Second Order. / Burova, I.G.; Alcybeev, G.O.

In: WSEAS Transactions on Applied and Theoretical Mechanics, Vol. 17, 2022, p. 258-262.

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

BibTeX

@article{8d32a5cb94544408b20a17a4ea0c4826,

title = "Solution of Integral Equations Using Local Splines of the Second Order",

abstract = "Splines are an important mathematical tool in Applied and Theoretical Mechanics. SeveralProblems in Mechanics are modeled with Differential Equations the solution of which demands Finite Elementsand Splines. In this paper, we consider the construction of computational schemes for the numerical solution ofintegral equations of the second kind with a weak singularity. To construct the numerical schemes, localpolynomial quadratic spline approximations and second-order nonpolynomial spline approximations are used. Theresults of the numerical experiments are given. This methodology has many applications in problems in Appliedand Theoretical Mechanics.",

keywords = "splines, integral equation of the second kind, weak singularity, local spline, polynomial spline, Nonpolynomial spline",

author = "I.G. Burova and G.O. Alcybeev",

year = "2022",

doi = "DOI: 10.37394/232011.2022.17.31",

language = "English",

volume = "17",

pages = "258--262",

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

issn = "1991-8747",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Solution of Integral Equations Using Local Splines of the Second Order

AU - Burova, I.G.

AU - Alcybeev, G.O.

PY - 2022

Y1 - 2022

N2 - Splines are an important mathematical tool in Applied and Theoretical Mechanics. SeveralProblems in Mechanics are modeled with Differential Equations the solution of which demands Finite Elementsand Splines. In this paper, we consider the construction of computational schemes for the numerical solution ofintegral equations of the second kind with a weak singularity. To construct the numerical schemes, localpolynomial quadratic spline approximations and second-order nonpolynomial spline approximations are used. Theresults of the numerical experiments are given. This methodology has many applications in problems in Appliedand Theoretical Mechanics.

AB - Splines are an important mathematical tool in Applied and Theoretical Mechanics. SeveralProblems in Mechanics are modeled with Differential Equations the solution of which demands Finite Elementsand Splines. In this paper, we consider the construction of computational schemes for the numerical solution ofintegral equations of the second kind with a weak singularity. To construct the numerical schemes, localpolynomial quadratic spline approximations and second-order nonpolynomial spline approximations are used. Theresults of the numerical experiments are given. This methodology has many applications in problems in Appliedand Theoretical Mechanics.

KW - splines

KW - integral equation of the second kind

KW - weak singularity

KW - local spline

KW - polynomial spline

KW - Nonpolynomial spline

U2 - DOI: 10.37394/232011.2022.17.31

DO - DOI: 10.37394/232011.2022.17.31

M3 - Article

VL - 17

SP - 258

EP - 262

JO - WSEAS Transactions on Applied and Theoretical Mechanics

JF - WSEAS Transactions on Applied and Theoretical Mechanics

SN - 1991-8747

ER -

ID: 103927266