时间分数阶扩散方程的隐式差分近似  

Implicit difference approximation for the time fractional order 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：《贵州师范大学学报（自然科学版）》2014年第2期79-82,共4页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(No.60673192);攀枝花学院校级培育项目(No.2012PY08)

摘　　要：考虑时间分数阶扩散方程,它是从标准的扩散方程中用分数阶导数α(0<α<1)代替一阶时间导数而得到,提出了一个计算有效的隐式差分近似,并证明了这个隐式差分近似是无条件稳定和无条件收敛的。最后给出了数值例子。Time fractional order diffusion equation was considered,which obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivation of order α（0 ＜α ＜ 1）.A computationally effective implicit difference approximation was proposed,and the fractional implicit difference approximation was proved unconditional stable and unconditional convergence.Finally,some numerical examples were given.

关 键 词：时间分数阶 扩散方程 隐武差分近似 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]