高阶微分算子的离散类比及其在寻找最优正交公式系数中的应用

IF 1.5 3区 数学 Q1 MATHEMATICS
K. M. Shadimetov, J. R. Davronov
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引用次数: 0

摘要

微分算子的离散类比在构建插值、正交和立方公式中发挥着重要作用。在这项研究中,我们考虑了专为偶数自然数 m 设计的微分算子 $\frac{d^{2m}}{dx^{2m}}+1$ 的离散类似算子 $D_{m}(h\beta)$,证明了该算子在 $L_{2}^{(2,0)}(0,1)$ 空间中构建最优正交公式的有效性。通过数值比较了最优正交公式在 $W_{2}^{(2,1)}(0,1)$ 空间和 $L_{2}^{(2,0)}(0,1)$ 空间中的误差。数值结果表明,与在 $W_{2}^{(2,1)}(0,1)$ 空间中构建的公式相比,本文构建的最优正交公式误差更小。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The discrete analogue of high-order differential operator and its application to finding coefficients of optimal quadrature formulas
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 $D_{m}(h\beta )$ of the differential operator $\frac{d^{2m}}{dx^{2m}}+1$ designed specifically for even natural numbers m. The operator’s effectiveness in constructing an optimal quadrature formula in the $L_{2}^{(2,0)}(0,1)$ space is demonstrated. The errors of the optimal quadrature formula in the $W_{2}^{(2,1)}(0,1)$ space and in the $L_{2}^{(2,0)}(0,1)$ 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 $W_{2}^{(2,1)}(0,1)$ space.
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来源期刊
自引率
6.20%
发文量
136
期刊介绍: The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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