Numerical methods for the forward and backward problems of a time-space fractional diffusion equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-21 DOI:10.1007/s10092-024-00567-3

Xiaoli Feng, Xiaoyu Yuan, Meixia Zhao, Zhi Qian

引用次数: 0

Abstract

In this paper, we consider the numerical methods for both the forward and backward problems of a time-space fractional diffusion equation. For the two-dimensional forward problem, we propose a finite difference method. The stability of the scheme and the corresponding Fast Preconditioned Conjugated Gradient algorithm are given. For the backward problem, since it is ill-posed, we use a quasi-boundary-value method to deal with it. Based on the Fourier transform, we obtain two kinds of order optimal convergence rates by using an a-priori and an a-posteriori regularization parameter choice rules. Numerical examples for both forward and backward problems show that the proposed numerical methods work well.

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时空分数扩散方程前向和后向问题的数值方法

本文考虑了时空分数扩散方程的正向和反向问题的数值方法。对于二维正向问题，我们提出了一种有限差分法。给出了方案的稳定性和相应的快速预处理共轭梯度算法。对于后向问题，由于它是一个求解困难的问题，我们采用了一种准界值方法来处理它。基于傅立叶变换，我们利用先验正则化参数选择规则和后验正则化参数选择规则，得到了两种阶最优收敛率。前向问题和后向问题的数值实例表明，所提出的数值方法效果良好。

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.