双边空间分数阶反常扩散方程的加权有限差分解法  

Weighted Finite Difference Methods for Two-Sided Space Fractional Anomalous Diffusion Equation

作　　者：马亮亮[1] 

机构地区：[1]攀枝花学院数学与计算机学院,四川攀枝花617000

出　　处：《中北大学学报（自然科学版）》2014年第5期525-529,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60673192);攀枝花学院校级培育项目(2012PY08)

摘　　要：在一般空间分数阶反常扩散方程的基础上,研究了一类含有初边值条件的双边空间分数阶反常扩散方程的有限差分问题.利用能量估计方法验证了所提出的加权有限差分格式是条件稳定的.借助于数学归纳法证明了在相同条件下所提出的加权有限差分格式是收敛的.最后,通过一个数值例子验证了所提出的加权有限差分格式是可靠和有效的.On the basis of the classical space fractional anomalous diffusion equation, a weighted finite differ- ence problem for two-sided space fractional anomalous diffusion equation with initial boundary value was inves- tigated. Then, using energy estimated method, the weighted finite difference scheme was proved conditional stable, and the convergence of the weighted finite difference scheme was also proved convergent by mathemat- ical induction under the same condition. Finally, a numerical example was included to demonstrate the validity and reliability of the scheme.

关 键 词：分数阶反常扩散方程 空间分数阶导数 加权差分格式 能量估计法 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]