Fractional difference/finite element approximations for the time-space fractional telegraph equation
Fractional difference/finite element approximations for the time-space fractional telegraph equation
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DOI：
10.1016/j.amc.2012.09.022
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发表时间：
2012-11-25
影响因子：
4
通讯作者：
Li, Changpin
中科院分区：
文献类型：
--
作者：
Zhao, Zhengang;Li, Changpin
本文研究了时空分数阶的数值解法（分数阶）电报方程，可用于电信号传输和传播的信号分析，以及反应扩散和悬浮流的无规行走等的建模，分析了半离散和全离散的数值逼近，其中空间1 + beta阶Riemann-Liouville分数阶导数的Galerkin有限元方法是（1，2）元，时间α阶Caputo导数的有限差分格式是（1/2，1）元和2 α元.详细地给出了解的存在唯一性、数值稳定性和误差估计等结果。最后通过数值算例验证了理论分析的正确性。(C)2012 Elsevier Inc. All rights reserved.
In this paper, we study the numerical solution of the time-space fractional order (fractional for simplicity) telegraph equation, which can be used in signal analysis for transmission and propagation of electrical signals, also the modeling of the reaction diffusion and the random walk of suspension flows and so on. The semi-discrete and fully discrete numerical approximations are both analyzed, where the Galerkin finite element method for the spatial Riemann-Liouville fractional derivative with order 1 + beta is an element of (1, 2) and the finite difference schemes for the temporal Caputo derivatives with orders alpha is an element of (1/2, 1) and 2 alpha are analyzed respectively. Results on the existence and uniqueness of the solution, the numerical stability, and the error estimates are displayed in details. Numerical examples are included to confirm the theoretical analysis. (C) 2012 Elsevier Inc. All rights reserved.