NUMERICAL METHODS FOR THE VARIABLE-ORDER FRACTIONAL ADVECTION-DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

被引：450
|
作者：
Zhuang, P. [1 ]
Liu, F. [2 ,3 ]
Anh, V. [2 ]
Turner, I. [2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia
[3] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Guangdong, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2009年 / 47卷 / 03期
基金：
澳大利亚研究理事会; 中国国家自然科学基金;
关键词：
fractional derivative of variable order; nonlinear fractional advection-diffusion equation; finite difference methods; method of lines; extrapolation method; stability and convergence; DISPERSION EQUATIONS; FELLER SEMIGROUPS; APPROXIMATION; DIFFERENTIATION; OPERATORS;
D O I：
10.1137/080730597
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moveover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.
引用
收藏
页码：1760 / 1781
页数：22
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