An analysis of a second order difference scheme for the fractional subdiffusion system

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• 作者：Xiuling Hu ; ^a ; ^{xiulinghu@126.com" class="auth_mail" title="E-mail the corresponding author} ; Luming Zhang^b
• 关键词：Subdiffusion system ; Implicit difference scheme ; Stability ; Convergence
• 刊名：Applied Mathematical Modelling
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：40
• 期：2
• 页码：1634-1649
• 全文大小：586 K

文摘

In this paper, an implicit finite difference method is explored for the fractional subdiffusion system. The method is proved to be uniquely solvable, stable and convergent when 0<γ≤log₂3−1$0<\gamma \le {\log }_{2}3-1$ with the order of O(τ²+h²)$O({\tau }^2+h^2)$ in L_∞ norm by the energy method with some novel skilled processing. Numerical experiments show that the scheme is second-order accuracy in temporal direction and can reduce the storage requirement and CPU time. The capability upon physical simulation of the scheme is good and it can be used to imitate the subdiffusive process of the fractional dynamical system.