Optimal quadrature formula in the sense of Sard in K2(P3) space | Zendy

Abdullo Hayotov | Zendy; Gradimir V. Milovanović | Zendy; Kholmat Shadimetov | Zendy

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Optimal quadrature formula in the sense of Sard in K2(P3) space

Author(s) -

Abdullo Hayotov,

Gradimir V. Milovanović,

Kholmat Shadimetov

Publication year - 2014

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1409029h

Subject(s) - mathematics , sobolev space , quadrature (astronomy) , gauss–kronrod quadrature formula , gauss–jacobi quadrature , clenshaw–curtis quadrature , mathematical analysis , trigonometry , tanh sinh quadrature , hilbert space , gaussian quadrature , nyström method , integral equation , electrical engineering , engineering

We construct an optimal quadrature formula in the sense of Sard in the Hilbert space K2(P3). Using Sobolev's method we obtain new op- timal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of the convergence of the optimal formula and prove an asymptotic optimality of such a formula in the Sobolev space L (3) (0, 1). The obtained optimal quadrature formula is exact for the trigonometric functions sinx, cosx and for constants. Also, we include a few numerical examples in order to illustrate the application of the obtained optimal quadrature formula.

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