抛物方程的可变两步 BDF 法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-01 DOI:10.1007/s10543-024-01007-y

Georgios Akrivis, Minghua Chen, Jianxing Han, Fan Yu, Zhimin Zhang

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引用次数: 0

摘要

研究了变网格上的两步后向差分公式法（BDF），该方法适用于具有自共轭椭圆部分的抛物方程。Becker (BIT 38:644-662, 1998) 和 Emmrich (J Appl Math Comput 19:33-55, 2005) 通过单乘法器能量技术分别证明了相邻时步比\(r_j:=k_j/k_{j-1}\leqslant 1.8685\) 和 1.9104 的标准稳定性估计值。即使略微提高比率也很麻烦。在本文中，我们提出了一种新技术，用于检验既非 Toeplitz 也非弱对角主导的带状矩阵的正定性；这一结果可视为 Grenander-Szegő 定理的变体。然后，利用两个乘数的能量技术，我们建立了相邻时步比高达 1.9398 的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The variable two-step BDF method for parabolic equations

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The variable two-step BDF method for parabolic equations

The two-step backward difference formula (BDF) method on variable grids for parabolic equations with self-adjoint elliptic part is considered. Standard stability estimates for adjacent time-step ratios \(r_j:=k_j/k_{j-1}\leqslant 1.8685\) and 1.9104, respectively, have been proved by Becker (BIT 38:644–662, 1998) and Emmrich (J Appl Math Comput 19:33–55, 2005) by the energy technique with a single multiplier. Even slightly improving the ratio is cumbersome. In this paper, we present a novel technique to examine the positive definiteness of banded matrices that are neither Toeplitz nor weakly diagonally dominant; this result can be viewed as a variant of the Grenander–Szegő theorem. Then, utilizing the energy technique with two multipliers, we establish stability for adjacent time-step ratios up to 1.9398.

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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.