摘要
在有限区域内考虑具有初边值问题的Riesz空间分数阶扩散方程,传统扩散方程中的二阶空间导数由Riesz分数阶导数α(1<α≤2)代替就得到Riesz空间分数阶扩散方程.我们提出一个在时间和空间都具有二阶精度的隐式方法,这个方法基于古典的Crank-Nicholson方法与空间外推方法,该隐式方法是无条件稳定和收敛的.最后给出一些数值例子来证实格式是高阶收敛的,此技巧可应用于解其它分数阶微分方程.
In this paper a Riesz space fractional diffusion equation on a finite domain is considered. This equation is obtained from the classical diffusion equation by replacing the second order derivative in space by a Riesz fractional derivative of order a （1〈a≤2）. An implicit method, which is second order accurate in time and in space, was proposed. This method was based on the classical Crank- Nicholson method combined with spatial extrapolation. It was proved that the implicit method was unconditionally stable and convergent. Finally, some numerical results were presented to demonstrate that our method was high order numerical method. This technique could be applied to solve other fractional differential equations.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第3期317-321,共5页
Journal of Xiamen University：Natural Science
基金
福建省自然科学基金(A0610025
A0410021)
集美大学博士科研经费(ZQ2006034)资助
关键词
空间分数阶扩散方程
隐式方法
二阶精度
稳定性
收敛性
Riesz space fractional diffusion equation
implicit method
second order accurate
stability
convergence
