An efficient conservative splitting characteristic difference method for solving 2-d space-fractional advection–diffusion equations

被引:0
|
作者
Ning Wang
Xinxia Zhang
Zhongguo Zhou
Hao Pan
Yan Wang
机构
[1] Shandong Agricultural University,School of Information Science and Engineering
来源
Computational and Applied Mathematics | 2023年 / 42卷
关键词
Spatial-fractional; PPM; Characteristic difference method; Stability; Error estimate; 65A05; 47F05; 35A05;
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学科分类号
摘要
In this paper, we develop an efficient splitting characteristic difference method for solving 2-dimensional two-sided space-fractional advection–diffusion equation. The intermediate numerical solutions are first computed by the piecewise parabolic method (PPM) where x¯i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{x}_i$$\end{document} is solved by the explicit second-order Runge–Kutta scheme. Then, the interior solutions are computed by the splitting σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-implicit characteristic difference method. By some auxiliary lemmas, our scheme is proved stable in L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document}-norm. The error estimate is given and we prove our schemes are of second-order convergence in space. Numerical experiments are used to verify our theoretical analysis.
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