Approximations with polynomial, trigonometric, exponential splines of the third order and boundary value problem

Standard

Approximations with polynomial, trigonometric, exponential splines of the third order and boundary value problem. / Burova, I. G.; Muzafarova, E. F.

в: International Journal of Circuits, Systems and Signal Processing, Том 14, 2020, стр. 460-473.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{82cc988c75c34e7ea422294ef3945f93,

title = "Approximations with polynomial, trigonometric, exponential splines of the third order and boundary value problem",

abstract = "—This paper is devoted to the construction of local approximations of functions of one and two variables using the polynomial, the trigonometric, and the exponential splines. These splines are useful for visualizing flows of graphic information. Here, we also discuss the parallelization of computations. Some attention is paid to obtaining two-sided estimates of the approximations using interval analysis methods. Particular attention is paid to solving the boundary value problem by using the polynomial splines and the trigonometric splines of the third and fourth order approximation. Using the considered splines, formulas for a numerical differentiation are constructed. These formulas are used to construct computational schemes for solving a parabolic problem. Questions of approximation and stability of the obtained schemes are considered. Numerical examples are presented.",

keywords = "Boundary value problem, Exponential splines, Interpolation, Interval estimation, Polynomial splines, Trigonometric splines",

author = "Burova, {I. G.} and Muzafarova, {E. F.}",

year = "2020",

doi = "10.46300/9106.2020.14.61",

language = "English",

volume = "14",

pages = "460--473",

journal = "International Journal of Circuits, Systems and Signal Processing",

issn = "1998-4464",

publisher = "North Atlantic University Union NAUN",

}

RIS

TY - JOUR

T1 - Approximations with polynomial, trigonometric, exponential splines of the third order and boundary value problem

AU - Burova, I. G.

AU - Muzafarova, E. F.

PY - 2020

Y1 - 2020

N2 - —This paper is devoted to the construction of local approximations of functions of one and two variables using the polynomial, the trigonometric, and the exponential splines. These splines are useful for visualizing flows of graphic information. Here, we also discuss the parallelization of computations. Some attention is paid to obtaining two-sided estimates of the approximations using interval analysis methods. Particular attention is paid to solving the boundary value problem by using the polynomial splines and the trigonometric splines of the third and fourth order approximation. Using the considered splines, formulas for a numerical differentiation are constructed. These formulas are used to construct computational schemes for solving a parabolic problem. Questions of approximation and stability of the obtained schemes are considered. Numerical examples are presented.

AB - —This paper is devoted to the construction of local approximations of functions of one and two variables using the polynomial, the trigonometric, and the exponential splines. These splines are useful for visualizing flows of graphic information. Here, we also discuss the parallelization of computations. Some attention is paid to obtaining two-sided estimates of the approximations using interval analysis methods. Particular attention is paid to solving the boundary value problem by using the polynomial splines and the trigonometric splines of the third and fourth order approximation. Using the considered splines, formulas for a numerical differentiation are constructed. These formulas are used to construct computational schemes for solving a parabolic problem. Questions of approximation and stability of the obtained schemes are considered. Numerical examples are presented.

KW - Boundary value problem

KW - Exponential splines

KW - Interpolation

KW - Interval estimation

KW - Polynomial splines

KW - Trigonometric splines

UR - http://www.scopus.com/inward/record.url?scp=85089606448&partnerID=8YFLogxK

U2 - 10.46300/9106.2020.14.61

DO - 10.46300/9106.2020.14.61

M3 - Article

AN - SCOPUS:85089606448

VL - 14

SP - 460

EP - 473

JO - International Journal of Circuits, Systems and Signal Processing

JF - International Journal of Circuits, Systems and Signal Processing

SN - 1998-4464

ER -

ID: 70070203