A new difference scheme for the time fractional diffusion equation

被引：637
|
作者：
Alikhanov, Anatoly A. [1 ]
机构：
[1] Kabardino Balkarian State Univ, Nalchik 360004, Russia
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2015年 / 280卷
基金：
俄罗斯基础研究基金会;
关键词：
Fractional diffusion equation; Finite difference method; Stability; Convergence; BOUNDARY-VALUE-PROBLEMS; VARIABLE-ORDER;
D O I：
10.1016/j.jcp.2014.09.031
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper we construct a new difference analog of the Caputo fractional derivative (called the L2-1(sigma) formula). The basic properties of this difference operator are investigated and on its basis some difference schemes generating approximations of the second and fourth order in space and the second order in time for the time fractional diffusion equation with variable coefficients are considered. Stability of the suggested schemes and also their convergence in the grid L-2-norm with the rate equal to the order of the approximation error are proved. The obtained results are supported by the numerical calculations carried out for some test problems. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：424 / 438
页数：15
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