Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term

被引：34

作者：

Chen, Chang-Ming ^{[2
]}

Liu, F. ^{[1
]}

Anh, V. ^{[1
]}

Turner, I. ^{[1
]}

机构：

[1] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 12期

基金：

澳大利亚研究理事会;

关键词：

The variable-order Galilei invariant advection diffusion equation with a nonlinear source term; The variable-order Riemann-Liouville fractional partial derivative; Stability; Convergence; Numerical scheme improving temporal accuracy; FRACTIONAL DIFFUSION; ANOMALOUS DIFFUSION; RANDOM-WALKS; SUBDIFFUSION; DIFFERENTIATION; TRANSPORT; STABILITY; ACCURACY; FIELDS;

D O I：

10.1016/j.amc.2010.12.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Finally, some numerical examples are given and the results demonstrate the effectiveness of theoretical analysis. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：5729 / 5742

页数：14

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