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Abstract The discrete analog of the differential operator plays a significant role in constructing interpolation, quadrature, and cubature formulas. In this work, we consider a discrete analog D₌ (h) D m (h β) of the differential operator d^2mdx^{2m}+1 d 2 m d x 2 m + 1 designed specifically for even natural numbers m. The operator’s effectiveness in constructing an optimal quadrature formula in the L₂^ (2, 0) (0, 1) L 2 (2, 0) (0, 1) space is demonstrated. The errors of the optimal quadrature formula in the W₂^ (2, 1) (0, 1) W 2 (2, 1) (0, 1) space and in the L₂^ (2, 0) (0, 1) L 2 (2, 0) (0, 1) space are compared numerically. The numerical results indicate that the optimal quadrature formula constructed in this work has a smaller error than the one constructed in the W₂^ (2, 1) (0, 1) W 2 (2, 1) (0, 1) space.
Shadimetov et al. (Tue,) studied this question.