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A New Numerical Approach for Solving 1D Fractional Diffusion-Wave Equation
Journal of Function Spaces ( IF 1.9 ) Pub Date : 2021-01-06 , DOI: 10.1155/2021/6638597
Mostafa M. A. Khater 1, 2 , Umair Ali 3 , Muhammad Asim Khan 4 , A. A. Mousa 5, 6 , Raghda A. M. Attia 7
Affiliation  

Fractional derivative is nonlocal, which is more suitable to simulate physical phenomena and provides more accurate models of physical systems such as earthquake vibration and polymers. The present study suggested a new numerical approach for the fractional diffusion-wave equation (FDWE). The fractional-order derivative is in the Riemann-Liouville (R-L) sense. Discussed the theoretical analysis of stability, consistency, and convergence. The numerical examples demonstrate that the method is more workable and excellently holds the theoretical analysis, showing the scheme’s feasibility.

中文翻译:

一维分数阶扩散波方程求解的新数值方法

分数导数是非局部的,它更适合于模拟物理现象,并提供物理系统(如地震振动和聚合物)的更精确模型。本研究为分数扩散波方程(FDWE)提出了一种新的数值方法。分数阶导数在Riemann-Liouville(RL)的意义上。讨论了稳定性,一致性和收敛性的理论分析。数值算例表明,该方法是可行的,并且很好地保留了理论分析,表明了该方案的可行性。
更新日期:2021-01-06
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