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

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.