Optimization of Quadrature Formulas in the Sobolev Space \(W_2^{(m)}(0,1)\)

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DOI: https://doi.org/10.28924/2291-8639-24-2026-328
Published: Oct 5, 2026
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Kh.M. Shadimetov, Sh.Sh. Ulikov, Optimization of Quadrature Formulas in the Sobolev Space \(W_2^{(m)}(0,1)\), Int. J. Anal. Appl., 24 (2026), 328.

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Kh.M. Shadimetov, Sh.Sh. Ulikov

Abstract

It is known that in many scientific and engineering problems the integration of functions constitutes an essential part of solving the complete problem. The construction of optimal quadrature formulas for the approximate evaluation of definite integrals on classes of functions is an essential part of this problem. In the present work, optimal quadrature formulas in the Sobolev space \(W_2^{(m)}(0,1)\) are constructed. Here the optimal coefficients of the quadrature formulas are found in the cases \(m=1\), \(m=2\), and \(m=3\). In addition, in the space \(W_2^{(1)}(0,1)\) the square of the norm of the error functional of the optimal quadrature formulas is computed.

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