Implicit difference approximation for the time fractional diffusion equation
Implicit difference approximation for the time fractional diffusion equation
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DOI：
10.1007/bf02832039
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发表时间：
2006-10
影响因子：
2.2
通讯作者：
P. Zhuang;Fawang Liu;Fawang Liu
中科院分区：
文献类型：
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作者：
P. Zhuang;Fawang Liu;Fawang Liu
本文考虑了有限区域上的一类时间分数阶扩散方程。该方程是从标准扩散方程出发，用分数阶导数(0<；α<；1)代替一阶时间导数得到的。我们提出了一种计算上有效的隐式差分近似来求解时间分数阶扩散方程。讨论了该方法的稳定性和收敛问题。我们证明了隐式差分近似是无条件稳定的，并且隐式差分近似收敛于O(Τ+H2)，其中Τ和Hare分别是时间步长和空间步长。文中给出了一些数值算例，说明了该方法的应用。
In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order 0 < α < 1 ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent withO(Τ +h2), where Τ andhare time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.