The discrete analogue of high-order differential operator and its application to finding coefficients of optimal quadrature formulas

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-02 DOI:10.1186/s13660-024-03111-7

K. M. Shadimetov, J. R. Davronov

引用次数: 0

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 $D_{m}(h\beta )$ 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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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

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。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.