非线性时间分数阶Schrödinger方程的线性化变换$L1$ Galerkin fem的无条件收敛性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-06-01 DOI:10.4208/nmtma.oa-2022-0087

Wanqiu Yuan, Dongfang Li null, C. Zhang

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引用次数: 7

摘要

.提出了一种线性化变换的L1伽辽金有限元法（FEM），用于数值求解多维时间分数阶Schr¨odinger方程。证明了完全离散格式的无条件最优误差估计。这种误差估计是通过结合一个新的离散分数Gr¨onwall不等式、相应的Sobolev嵌入定理和一些逆不等式得到的。而先前的无条件收敛结果通常是通过使用时空误差吐出方法来获得的。给出了数值例子来证实理论结果

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Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations

. A linearized transformed L 1 Galerkin ﬁnite element method (FEM) is presented for numerically solving the multi-dimensional time fractional Schr¨odinger equations. Unconditionally optimal error estimates of the fully-discrete scheme are proved. Such error estimates are obtained by combining a new discrete fractional Gr¨onwall inequality, the corresponding Sobolev embedding theorems and some inverse inequalities. While the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting approaches. Numerical examples are presented to conﬁrm the theoretical results

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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.

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