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Jan 2017 Time evolution of the approximate and stationary solutions of the Time-Fractional Forced-Damped-Wave equation
A. M. A. El-Sayed, E. A. Abdel-Rehim, A. S. Hashem
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Tbilisi Math. J. 10(1): 127-144 (Jan 2017). DOI: 10.1515/tmj-2017-0008

Abstract

In this paper, the simulation of the time-fractional-forced-damped-wave equation (the diffusion advection forced wave) is given for different parameters. The common finite difference rules beside the backward Grünwald–Letnikov scheme are used to find the approximation solution of this model. The paper discusses also the effects of the memory, the internal force (resistance) and the external force on the travelling wave. We follow the waves till they reach their stationary waves. The Von-Neumann stability condition is also considered and discussed. Besides the simulation of the time evolution of the approximation solution of the classical and time-fractional model, the stationary solutions are also simulated. All the numerical results are compared for different values of time.

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A. M. A. El-Sayed. E. A. Abdel-Rehim. A. S. Hashem. "Time evolution of the approximate and stationary solutions of the Time-Fractional Forced-Damped-Wave equation." Tbilisi Math. J. 10 (1) 127 - 144, Jan 2017. https://doi.org/10.1515/tmj-2017-0008

Information

Received: 17 June 2016; Accepted: 8 July 2016; Published: Jan 2017
First available in Project Euclid: 26 May 2018

zbMATH: 1364.35422
MathSciNet: MR3610025
Digital Object Identifier: 10.1515/tmj-2017-0008

Subjects:
Primary: 26A33
Secondary: 35J05, 35L05, 42A38, 45K05, 60G50, 60G51, 60J60, 65N06

Rights: Copyright © 2017 Tbilisi Centre for Mathematical Sciences

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Vol.10 • No. 1 • Jan 2017
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