The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves

The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves

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In this paper is considered the extreme problem of searching for the optimal quadrature formulas in S.M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm of which in Lp (1 ≤ p < ∞) is bounded...

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Main Author: K. Tukhliev
Format: Article
Language:English
Published: Yaroslavl State University 2013-06-01
Series:Modelirovanie i Analiz Informacionnyh Sistem
Subjects:
quadrature formula
curvilinear integral
gradient
error
node
Online Access:https://www.mais-journal.ru/jour/article/view/200
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spelling doaj-9ec91148e78e41969a4f9fe05d08be3b2021-07-29T08:15:18ZengYaroslavl State UniversityModelirovanie i Analiz Informacionnyh Sistem1818-10152313-54172013-06-0120312112910.18255/1818-1015-2013-3-121-129194The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and CurvesK. Tukhliev0Khujand State UniversityIn this paper is considered the extreme problem of searching for the optimal quadrature formulas in S.M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm of which in Lp (1 ≤ p < ∞) is bounded along the curve by which the curvilinear integral is calculated. The exact errors of optimal quadrature formula for the studied class of functions were calculated, and the explicit formulas for optimal nodes and coefficients was shown.https://www.mais-journal.ru/jour/article/view/200quadrature formulacurvilinear integralgradienterrornode
collection DOAJ
language English
format Article
sources DOAJ
author K. Tukhliev
spellingShingle K. Tukhliev
The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
Modelirovanie i Analiz Informacionnyh Sistem
quadrature formula
curvilinear integral
gradient
error
node
author_facet K. Tukhliev
author_sort K. Tukhliev
title The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
title_short The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
title_full The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
title_fullStr The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
title_full_unstemmed The Optimal Quadrature Formula of Approximate Calculation of Curvilinear Integral of First Kind for Some Classes of Functions and Curves
title_sort optimal quadrature formula of approximate calculation of curvilinear integral of first kind for some classes of functions and curves
publisher Yaroslavl State University
series Modelirovanie i Analiz Informacionnyh Sistem
issn 1818-1015
2313-5417
publishDate 2013-06-01
description In this paper is considered the extreme problem of searching for the optimal quadrature formulas in S.M. Nikolskiy sense for approximate calculation of curvilinear integrals of first kind on the class of differentiable functions, the second gradient norm of which in Lp (1 ≤ p < ∞) is bounded along the curve by which the curvilinear integral is calculated. The exact errors of optimal quadrature formula for the studied class of functions were calculated, and the explicit formulas for optimal nodes and coefficients was shown.
topic quadrature formula
curvilinear integral
gradient
error
node
url https://www.mais-journal.ru/jour/article/view/200
work_keys_str_mv AT ktukhliev theoptimalquadratureformulaofapproximatecalculationofcurvilinearintegraloffirstkindforsomeclassesoffunctionsandcurves
AT ktukhliev optimalquadratureformulaofapproximatecalculationofcurvilinearintegraloffirstkindforsomeclassesoffunctionsandcurves
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