Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
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DOI：
10.1016/j.cam.2009.02.013
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发表时间：
2009-09-01
影响因子：
2.4
通讯作者：
Burrage, K.
中科院分区：
文献类型：
--
作者：
Liu, F.;Yang, C.;Burrage, K.
在本文中，我们考虑一种带有非线性源项的修正反常次扩散方程，用于描述通过包含作用于扩散项的第二分数时间导数而随着时间的推移变得不那么反常的过程。构造了一种新的隐式差分方法。使用新的能量方法讨论了稳定性和收敛性。最后给出了一些数值例子。数值结果证明了理论分析的有效性。 (C) 2009 Elsevier B.V. 保留所有权利。
In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis. (C) 2009 Elsevier B.V. All rights reserved.