The Local Nonpolynomial Splines and Solution of Integro-Differential Equations

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The Local Nonpolynomial Splines and Solution of Integro-Differential Equations. / Burova, I.G.

In: WSEAS Transactions on Mathematics, Vol. 21, 24.10.2022, p. 718-730.

Research output: Contribution to journal › Conference article › peer-review

BibTeX

@article{ca25bc514791408ba6280b9069d95f6b,

title = "The Local Nonpolynomial Splines and Solution of Integro-Differential Equations",

abstract = "The application of the local polynomial splines to the solution of integro-differential equations was regarded in the author{\textquoteright}s previous papers. In a recent paper, we introduced the application of the local nonpolynomial splines to the solution of integro-differential equations. These splines allow us to approximatefunctions with a presribed order of approximation. In this paper, we apply the splines to the solution of the integro-differential equations with a smooth kernel. Applying the trigonometric or exponential spline approximations of the fifth order of approximation, we obtain an approximate solution of the integrodifferential equation at the set of nodes. The advantages of using such splines include the ability to determine not only the values of the desired function at the grid nodes, but also the first derivative at the grid nodes. The obtained values can be connected by lines using the splines. Thus, after interpolation, we can obtain the value of the solution at any point of the considered interval. Several numerical examples are given.",

keywords = "Local nonpolynomial splines, local trigonometric splines, local exponential splines, integrodifferential equations, the fifth order of approximation",

author = "I.G. Burova",

year = "2022",

month = oct,

day = "24",

doi = "10.37394/23206.2022.21.84",

language = "English",

volume = "21",

pages = "718--730",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

note = "International Conference on Mathematical Models & Computational Techniques in Science & Engineering, MMCTSE 2022 ; Conference date: 22-08-2022 Through 24-08-2022",

}

RIS

TY - JOUR

T1 - The Local Nonpolynomial Splines and Solution of Integro-Differential Equations

AU - Burova, I.G.

PY - 2022/10/24

Y1 - 2022/10/24

N2 - The application of the local polynomial splines to the solution of integro-differential equations was regarded in the author’s previous papers. In a recent paper, we introduced the application of the local nonpolynomial splines to the solution of integro-differential equations. These splines allow us to approximatefunctions with a presribed order of approximation. In this paper, we apply the splines to the solution of the integro-differential equations with a smooth kernel. Applying the trigonometric or exponential spline approximations of the fifth order of approximation, we obtain an approximate solution of the integrodifferential equation at the set of nodes. The advantages of using such splines include the ability to determine not only the values of the desired function at the grid nodes, but also the first derivative at the grid nodes. The obtained values can be connected by lines using the splines. Thus, after interpolation, we can obtain the value of the solution at any point of the considered interval. Several numerical examples are given.

AB - The application of the local polynomial splines to the solution of integro-differential equations was regarded in the author’s previous papers. In a recent paper, we introduced the application of the local nonpolynomial splines to the solution of integro-differential equations. These splines allow us to approximatefunctions with a presribed order of approximation. In this paper, we apply the splines to the solution of the integro-differential equations with a smooth kernel. Applying the trigonometric or exponential spline approximations of the fifth order of approximation, we obtain an approximate solution of the integrodifferential equation at the set of nodes. The advantages of using such splines include the ability to determine not only the values of the desired function at the grid nodes, but also the first derivative at the grid nodes. The obtained values can be connected by lines using the splines. Thus, after interpolation, we can obtain the value of the solution at any point of the considered interval. Several numerical examples are given.

KW - Local nonpolynomial splines

KW - local trigonometric splines

KW - local exponential splines

KW - integrodifferential equations

KW - the fifth order of approximation

UR - https://www.mendeley.com/catalogue/bdb18534-af53-320f-b8c0-760499785ba7/

U2 - 10.37394/23206.2022.21.84

DO - 10.37394/23206.2022.21.84

M3 - Conference article

VL - 21

SP - 718

EP - 730

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

T2 - International Conference on Mathematical Models & Computational Techniques in Science & Engineering

Y2 - 22 August 2022 through 24 August 2022

ER -

ID: 101054404