The discrete analogue of a differential operator and its applications |
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| Authors: | Abdullo Rakhmonovich Hayotov |
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| Affiliation: | 1. Institute of Mathematics, National University of Uzbekistan, Do’rmon yo’li str. 29, Tashkent, 100125, Uzbekistan
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| Abstract: | ![]()
We construct a discrete analogue D m (hβ) of the differential operator d2m /dx 2m + 2ω 2d2m?2 /dx 2m?2 + ω 4d2m?4 /dx 2m?4 for any m ≥ 2. In the case m = 2, we apply in the Hilbert space K 2(P 2) the discrete analogue D 2(hβ) for construction of optimal quadrature formulas and interpolation splines minimizing the seminorm, which are exact for trigonometric functions sin ωx and cos ωx. |
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