Numerical approximations for fractional diffusion equations via splines

被引：80
|
作者：
Sousa, Ercilia [1 ]
机构：
[1] Univ Coimbra, CMUC, Dept Math, P-3001454 Coimbra, Portugal
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 03期
关键词：
Fractional diffusion; Integro-differential equations; Finite differences; ADVECTION-DISPERSION EQUATION; FINITE-DIFFERENCE APPROXIMATIONS; TRANSPORT; STABILITY;
D O I：
10.1016/j.camwa.2011.04.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A one-dimensional fractional diffusion model is considered, where the usual second order derivative gives place to a fractional derivative of order alpha, with 1 < alpha <= 2. We consider the Caputo derivative as the space derivative, which is a form of representing the fractional derivative by an integral operator. An implicit numerical method is derived which uses a spline approximation for the Caputo derivative. The consistency and stability of the method are examined and numerical results are presented. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：938 / 944
页数：7
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