求解时变分数阶对流扩散方程的质心有理插值方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/era.2023205

Jin Li, Yongling Cheng

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引用次数: 1

摘要

采用质心有理插值法(BRIM)求解时变分数对流扩散方程。由于分数阶导数是非局部算子，我们采用谱法求解TFCD方程，得到系数矩阵为全矩阵。首先，将TFCD方程的分数阶导数从奇异核转化为密度函数的非奇异积分。其次，对新高斯公式进行高效求积分，简化计算。第三，将未知函数替换为质心有理插值基函数，得到离散的TFCD方程的矩阵方程。然后，证明了BRIM的收敛速度。最后，给出了一个数值算例来说明我们的结果。

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Barycentric rational interpolation method for solving time-dependent fractional convection-diffusion equation

The time-dependent fractional convection-diffusion (TFCD) equation is solved by the barycentric rational interpolation method (BRIM). Since the fractional derivative is the nonlocal operator, we develop a spectral method to solve the TFCD equation to get the coefficient matrix as a full matrix. First, the fractional derivative of the TFCD equation is changed to a nonsingular integral from the singular kernel to a density function. Second, efficient quadrature of the new Gauss formula are constructed to simply compute it. Third, matrix equation of discrete the TFCD equation is obtained by the unknown function replaced by a barycentric rational interpolation basis function. Then, the convergence rate of BRIM is proved. Finally, a numerical example is given to illustrate our result.

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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.