基于软化正则化的分数阶导数Jacobi谱计算方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-13 DOI:10.3233/asy-231869

Wen Zhang, Changxing Wu, Zhousheng Ruan, Shufang Qiu

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引用次数: 0

摘要

本文构造了一种基于Jacobi - gauss正交的近似Caputo分数阶导数的Jacobi谱配置方案。给出了各向异性Jacobi-weighted Sobolev空间的收敛性分析。在此基础上，给出了用安抚正则化方法求解含噪声数据的Caputo分数阶导数的收敛速度。最后，通过数值算例验证了该方法的有效性和稳定性。

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A Jacobi spectral method for calculating fractional derivative based on mollification regularization

In this article, we construct a Jacobi spectral collocation scheme to approximate the Caputo fractional derivative based on Jacobi–Gauss quadrature. The convergence analysis is provided in anisotropic Jacobi-weighted Sobolev spaces. Furthermore, the convergence rate is presented for solving Caputo fractional derivative with noisy data by invoking the mollification regularization method. Lastly, numerical examples illustrate the effectiveness and stability of the proposed method.

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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.