Simulation of the approximate solutions of the time-fractional multi-term wave equations

被引：13
|
作者：
Abdel-Rehim, E. A. [1 ]
El-Sayed, A. M. A. [2 ]
Hashem, A. S. [1 ]
机构：
[1] Suez Canal Univ, Fac Sci, Dept Math, Ismailia, Egypt
[2] Univ Alexandria, Dept Math, Fac Sci, Alexandria, Egypt
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 73卷 / 06期
关键词：
Approximation solution; Diffusion wave equation; Explicit scheme; Time fractional; Stability; Stationary solution; FREQUENCY POWER-LAW; DIFFUSION; MEDIA;
D O I：
10.1016/j.camwa.2016.06.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, simulations of the approximation solutions of time-fractional wave, forced wave (shear wave), and damped wave equations are given. The common finite difference rules besides the backward Grunwald-Letnikov scheme are used to find the approximation solution of these models. The paper discusses also the effects of the memory, the internal force (resistance) and the external force on the travelling wave. The Von-Neumann stability conditions are also considered and discussed for these models. Besides the simulations of the time evolutions of the approximation solutions, the stationary solutions are also simulated. The numerical results are obtained by the Mathematica software. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1134 / 1154
页数：21
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