Spectral Galerkin Methods for Riesz Space-Fractional Convection-Diffusion Equations

被引：3

作者：

Zhang, Xinxia ^{[1
]}

Wang, Jihan ^{[1
]}

Wu, Zhongshu ^{[1
]}

Tang, Zheyi ^{[1
]}

Zeng, Xiaoyan ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

FRACTAL AND FRACTIONAL | 2024年 / 8卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Riesz fractional derivatives; fractional convection-diffusion equation; spectral Galerkin method; DISTRIBUTED-ORDER; FUNDAMENTAL SOLUTION; ANOMALOUS DIFFUSION; RANDOM-WALK; CALCULUS; APPROXIMATION;

D O I：

10.3390/fractalfract8070431

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper applies the spectral Galerkin method to numerically solve Riesz space-fractional convection-diffusion equations. Firstly, spectral Galerkin algorithms were developed for one-dimensional Riesz space-fractional convection-diffusion equations. The equations were solved by discretizing in space using the Galerkin-Legendre spectral approaches and in time using the Crank-Nicolson Leap-Frog (CNLF) scheme. In addition, the stability and convergence of semi-discrete and fully discrete schemes were analyzed. Secondly, we established a fully discrete form for the two-dimensional case with an additional complementary term on the left and then obtained the stability and convergence results for it. Finally, numerical simulations were performed, and the results demonstrate the effectiveness of our numerical methods.

引用

页数：26

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