Article citationsMore >>

Shadimetov, Kh.M.: Optimal formulas of approximate integration for differentiable functions, Candidate dissertation, Novosibirsk, 1983, p. 140. arXiv:1005.0163v1 [NA.math].

has been cited by the following article:

Article

Optimal Quadrature Formulas with Polynomial Weight in Sobolev Space

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


American Journal of Numerical Analysis. 2014, Vol. 2 No. 5, 144-151
DOI: 10.12691/ajna-2-5-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Kholmat M. Shadimetov, Abdullo R. Hayotov, 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.

Correspondence to: Abdullo  R. Hayotov, Institute of Mathematics, National University of Uzbekistan, Do‘rmon yo‘li str., Tashkent, Uzbekistan. Email: hayotov@mail.ru

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