Application of non-polynomial splines to solving differential equations

Standard

Application of non-polynomial splines to solving differential equations. / Burova, I. G.

In: WSEAS Transactions on Mathematics, Vol. 19, 02.11.2020, p. 531-548.

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

BibTeX

@article{13652b8cbaf74e23bc1191d7f578ff14,

title = "Application of non-polynomial splines to solving differential equations",

abstract = "The application of the local polynomial and non-polynomial to the construction of methods for numerically solving the heat conduction problem is discussed. The non-polynomial splines are used here to approximate the partial derivatives. Formulas for numerical differentiation based on the application of the non-polynomial splines of the fourth order of approximation are constructed. Particular attention is paid to polynomial, trigonometric, exponential, polynomial-trigonometric and polynomial-exponential splines. This approach allows us to construct explicit and implicit difference schemes. The main focus of the paper is on implicit difference scheme. New approximations with splines of the Lagrange and Hermite type with new properties are obtained. These approximations take into account the first and second derivatives of the function being approximated. Numerical examples are given.",

keywords = "Exponential splines, Heat conduction problem, Polynomial splines, Polynomial-exponential splines, Polynomial-trigonometric splines, Trigonometric splines",

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

year = "2020",

month = nov,

day = "2",

doi = "10.37394/23206.2020.19.58",

language = "English",

volume = "19",

pages = "531--548",

journal = "WSEAS Transactions on Mathematics",

issn = "1109-2769",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

}

RIS

TY - JOUR

T1 - Application of non-polynomial splines to solving differential equations

AU - Burova, I. G.

PY - 2020/11/2

Y1 - 2020/11/2

N2 - The application of the local polynomial and non-polynomial to the construction of methods for numerically solving the heat conduction problem is discussed. The non-polynomial splines are used here to approximate the partial derivatives. Formulas for numerical differentiation based on the application of the non-polynomial splines of the fourth order of approximation are constructed. Particular attention is paid to polynomial, trigonometric, exponential, polynomial-trigonometric and polynomial-exponential splines. This approach allows us to construct explicit and implicit difference schemes. The main focus of the paper is on implicit difference scheme. New approximations with splines of the Lagrange and Hermite type with new properties are obtained. These approximations take into account the first and second derivatives of the function being approximated. Numerical examples are given.

AB - The application of the local polynomial and non-polynomial to the construction of methods for numerically solving the heat conduction problem is discussed. The non-polynomial splines are used here to approximate the partial derivatives. Formulas for numerical differentiation based on the application of the non-polynomial splines of the fourth order of approximation are constructed. Particular attention is paid to polynomial, trigonometric, exponential, polynomial-trigonometric and polynomial-exponential splines. This approach allows us to construct explicit and implicit difference schemes. The main focus of the paper is on implicit difference scheme. New approximations with splines of the Lagrange and Hermite type with new properties are obtained. These approximations take into account the first and second derivatives of the function being approximated. Numerical examples are given.

KW - Exponential splines

KW - Heat conduction problem

KW - Polynomial splines

KW - Polynomial-exponential splines

KW - Polynomial-trigonometric splines

KW - Trigonometric splines

UR - http://www.scopus.com/inward/record.url?scp=85096911733&partnerID=8YFLogxK

U2 - 10.37394/23206.2020.19.58

DO - 10.37394/23206.2020.19.58

M3 - Article

AN - SCOPUS:85096911733

VL - 19

SP - 531

EP - 548

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -

ID: 72515508