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American Journal of Numerical Analysis
ISSN (Print): 2372-2118 ISSN (Online): 2372-2126 Website: https://www.sciepub.com/journal/ajna Editor-in-chief: Emanuele Galligani
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American Journal of Numerical Analysis. 2014, 2(5), 144-151
DOI: 10.12691/ajna-2-5-2
Open AccessArticle

Optimal Quadrature Formulas with Polynomial Weight in Sobolev Space

Kholmat M. Shadimetov1, Abdullo R. Hayotov1, and Sardor I. Ismoilov1

1Institute of Mathematics, National University of Uzbekistan, Do‘rmon yo‘li str., Tashkent, Uzbekistan

Pub. Date: October 12, 2014
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Cite this paper:
Kholmat M. Shadimetov, Abdullo R. Hayotov and Sardor I. Ismoilov. Optimal Quadrature Formulas with Polynomial Weight in Sobolev Space. American Journal of Numerical Analysis. 2014; 2(5):144-151. doi: 10.12691/ajna-2-5-2

Abstract

In this paper we construct the optimal quadrature formula with polynomial weight in the Sobolev space L2(m)(0,1). Using S.L. Sobolev’s method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula.

Keywords:
optimal quadrature formulas error functional extremal function sobolev space optimal coefficients

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