Coefficients of optimal quadrature formulas in the space of differentiable functions
Kholmat ShadimetovTashkent State Transport University, 1, Odilkhodjaev street, Tashkent 100167, UzbekistanFarhod NuralievBukhara State University, 11, M.Ikbol str., Bukhara 200114, UzbekistanSiroj AzamovBukhara State University, 11, M.Ikbol str., Bukhara 200114, UzbekistanShukurillo UlikovV.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University street, Tashkent 100174, Uzbekistan
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Аннотация
In this paper, we consider the construction of an optimal lattice quadrature formula in the space W2(m)(0, 1). Further, finding the extremal function of the error functional of quadrature formulas, by virtue of the Riesz theorem on the general form of a linear continuous functional, is reduced to solving a boundary value problem for ordinary differential equations. Solving this boundary value problem, we obtain an explicit expression for the extremal function of the error functional of quadrature formulas. In addition, by virtue of the Riesz theorem, the square of the norm of the error functional is explicitly calculated and an analytical expression is obtained for the optimal coefficients of the quadrature formulas at m = 2.
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