@article{ajna2013114,
author={{Shadimetov, Kholmat M. and Hayotov, Abdullo R. and Akhmedov, Dilshod M.},
title={Optimal Quadrature Formulas for the Cauchy Type Singular Integral in the Sobolev Space <i>L</i><SUB>2</SUB><SUP>(2)</SUP>(-1,1)},
journal={American Journal of Numerical Analysis},
volume={1},
number={1},
pages={22--31},
year={2013},
url={http://pubs.sciepub.com/ajna/1/1/4},
abstract={This paper studies the problem of construction of the optimal quadrature formula in the sense of Sard in <i>L</i><SUB>2</SUB><SUP>(2)</SUP>(-1,1) S.L.Sobolev space for approximate calculation of the Cauchy type singular integral. Using the discrete analogue of the operator <i>d</i><SUP><i>4</i></SUP><i>/dx</i><SUP><i>4</i></SUP> 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].},
doi={10.12691/ajna-1-1-4}
publisher={Science and Education Publishing}
}