时间分数阶反应-扩散方程的隐式差分近似

Implicit Difference Approximation for the Time-fractional Order Reaction-diffusion Equation

考虑时间分数阶反应-扩散方程,它是从标准的反应-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.利用分数阶离散系数的特点,证明了这个隐式差分近似是无条件稳定的,并且也证明了它的收敛性.最后给出数值例子.

Time-fractional order reaction-diffusion equation was considered,which obtained from the standard reaction-diffusion equation by replacing the first-order time derivative by a fractional derivation of order a（0〈α〈1）. A computationally effective implicit difference approximation was proposed. Using the characteristic of the fractional discrete coefficient,the authors proved that the fractional implicit difference approximation was unconditional stable. Convergence of the approximation was also proved. Finally, some numerical examples were given.