经典Richardson外推在显式一步法中的一致性与收敛性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-19 DOI:10.3846/mma.2023.16283

Teshome Bayleyegn, I. Faragó, Ágnes Havasi

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引用次数: 1

摘要

本文分析了经典理查德森外推法(CRE)的一致性，这是一种简单而稳健的计算装置，其基础方法是一阶或二阶一致性常微分方程的显式一步数值方法。在经典框架中，CRE使一致性的阶数增加了1。通过假设基法的时间步进算子在其第二参数中具有Lipschitz性质，证明了方法的收敛性。

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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On the Consistency and convergence of Classical Richardson extrapolation as Applied to Explicit One-Step Methods

The consistency of the classical Richardson extrapolation (CRE), a simple and robust computational device, is analysed for the case where the underlying method is an explicit one-step numerical method for ordinary differential equations with order of consistency one or two. It is shown in the classical framework that the CRE increases the order of consistency by one. The convergence of the method is proved by the assumption that the time-stepping operator of the base method has the Lipschitz property in its second argument.

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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.