Joint scientific investigations with Uzbekistan Republic continue

   Within the framework of the Agreement on scientific cooperation, signed between IKIR FEB RAS and the Institute of Mathematics by V.I. Romanovskiy (Tashkent, Uzbekistan), the works in the field of mathematical investigations continue.

   A joint paper of the researchers of these institutes "Optimization of the Approximate Integration Formula Using the Discrete Analogue of a High-Order Differential Operator" by K. Shadimetov, A. Boltaev, R. Parovik has been published in Mathematics (July 2023) (https://doi.org/10.3390/math11143114).

    It is known that discrete analogs of differential operators play an important role in constructing optimal quadrature, cubature, and difference formulas. Using discrete analogs of differential operators, optimal interpolation, quadrature, and difference formulas exact for algebraic polynomials, trigonometric and exponential functions can be constructed. In this paper, we construct a discrete analogue D m ( h β ) of the differential operator d 2 m d x 2 m + 2 d m d x m + 1 in the Hilbert space W 2 ( m , 0 ) . We develop an algorithm for constructing optimal quadrature formulas exact on exponential-trigonometric functions using a discrete operator. Based on this algorithm, in m = 2 , we give an optimal quadrature formula exact for trigonometric functions. Finally, we present the rate of convergence of the optimal quadrature formula in the Hilbert space W 2 ( 2 , 0 ) for the case m = 2 .