eng
Science and Education Publishing
American Journal of Numerical Analysis
2013 Revised November 20, 2013 December 03, 2013--1-12
1
1
22
31
10.12691/ajna-1-1-4
AJNA2013114
article
Optimal Quadrature Formulas for the Cauchy Type Singular Integral in the Sobolev Space L2(2)(-1,1)
Kholmat M. Shadimetov
1
Abdullo R. Hayotov
hayotov@mail.ru
1
Dilshod M. Akhmedov
1
Department of Computational Methods, Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
This paper studies the problem of construction of the optimal quadrature formula in the sense of Sard in L2(2)(-1,1) S.L.Sobolev space for approximate calculation of the Cauchy type singular integral. Using the discrete analogue of the operator d4/dx4 we obtain new optimal quadrature formulas. Furthermore, explicit formulas of the optimal coefficients are obtained. Finally, in numerical examples, we give the error bounds obtained for the case h=0.02 by our optimal quadrature formula and compared with the corresponding error bounds of the quadrature formula (15) of the work [26] at different values of singular point t. The numerical results show that our quadrature formula is more accurate than the quadrature formula constructed in the work [26].
http://pubs.sciepub.com/ajna/1/1/4/ajna-1-1-4.pdf
optimal quadrature formulasingular integral of Cauchy typeSobolev space