A posteriori error estimates for the exponential midpoint method for linear and semilinear parabolic equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-19 DOI:10.1007/s11075-024-01940-7

Xianfa Hu, Wansheng Wang, Mengli Mao, Jiliang Cao

引用次数: 0

Abstract

In this paper, the a posteriori error estimates of the exponential midpoint method for time discretization are established for linear and semilinear parabolic equations. Using the exponential midpoint approximation defined by a continuous and piecewise linear interpolation of nodal values yields suboptimal order estimates. Based on the property of the entire function, we introduce a continuous and piecewise quadratic time reconstruction of the exponential midpoint method to derive optimal order estimates; the error bounds solely depend on the discretization parameters, the data of the problem, and the approximation of the entire function. Several numerical examples are implemented to illustrate the theoretical results.

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线性和半线性抛物方程指数中点法的后验误差估计

本文针对线性和半线性抛物线方程，建立了指数中点法时间离散化的后验误差估计。使用由节点值的连续分片线性插值定义的指数中点近似会产生次优阶次估计。基于整个函数的特性，我们引入了指数中点法的连续和片断二次时间重构，从而得出最优阶次估计值；误差边界完全取决于离散化参数、问题数据和整个函数的近似值。我们通过几个数值示例来说明理论结果。

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.