An application of Hayashi's inequality in numerical integration

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-12 DOI:10.1515/math-2023-0162

Ahmed Salem Heilat, Ahmad Qazza, Raed Hatamleh, Rania Saadeh, Mohammad W. Alomari

引用次数: 0

Abstract

This study systematically develops error estimates tailored to a specific set of general quadrature rules that exclusively incorporate first derivatives. Moreover, it introduces refined versions of select generalized Ostrowski’s type inequalities, enhancing their applicability. Through the skillful application of Hayashi’s celebrated inequality to specific functions, the provided proofs underpin these advancements. Notably, this approach extends its utility to approximate integrals of real functions with bounded first derivatives. Remarkably, it employs Newton-Cotes and Gauss-Legendre quadrature rules, bypassing the need for stringent requirements on higher-order derivatives.

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林不等式在数值积分中的应用

本研究系统地开发了误差估算，这些误差估算是为专门包含一阶导数的一组特定一般正交规则量身定制的。此外，它还引入了精选的广义奥斯特洛夫斯基式不等式，增强了它们的适用性。通过巧妙地将林氏著名不等式应用于特定函数，所提供的证明为这些进步奠定了基础。值得注意的是，这种方法将其实用性扩展到了具有有界一阶导数的实函数近似积分。值得注意的是，它采用了牛顿-科茨和高斯-勒根得尔正交规则，绕过了对高阶导数的严格要求。

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.