Numerical solution of fractional advection-diffusion equation with a nonlinear source term

被引：62
|
作者：
Parvizi, M. [1 ]
Eslahchi, M. R. [1 ]
Dehghan, Mehdi [2 ]
机构：
[1] Tarbiat Modares Univ, Fac Math Sci, Dept Appl Math, Tehran, Iran
[2] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, Tehran 15914, Iran
来源：
NUMERICAL ALGORITHMS | 2015年 / 68卷 / 03期
关键词：
Fractional advection-diffusion equation; Riemann-Liouville derivative; Jacobi polynomials; Operational matrix; Collocation method; Stability analysis and convergence; FINITE-DIFFERENCE APPROXIMATIONS; FUNDAMENTAL SOLUTION; ORDER;
D O I：
10.1007/s11075-014-9863-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we use the Jacobi collocation method for solving a special kind of the fractional advection-diffusion equation with a nonlinear source term. This equation is the classical advection-diffusion equation in which the space derivatives are replaced by the Riemann-Liouville derivatives of order 0 < sigma a parts per thousand currency sign 1 and 1 < mu a parts per thousand currency sign 2. Also the stability and convergence of the presented method are shown for this equation. Finally some numerical examples are solved using the presented method.
引用
收藏
页码：601 / 629
页数：29
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