What is it about?
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 Grunwald–Letnikov scheme are used to find the approximation solution of this model.
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Why is it important?
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 Grunwald–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.
Perspectives
We have studied numerically the time evolution of the approximation solution of the time–fractional– forced–damped-wave equation . We have plotted the approximation solutions for different values. The analytical stationary solution is also plotted and compared with the stationary approximation solution. The results show that the wave forced damped equation behaves exactly as the diffusion equation as t -> infinity which is expected. This model has an important applications in physics , mathematics and medical applications.
amel hashem
faculty of science-suez canal university-egypt
Read the Original
This page is a summary of: Time evolution of the approximate and stationary solutions of the Time-Fractional Forced-Damped-Wave equation, Tbilisi Mathematical Journal, January 2017, De Gruyter,
DOI: 10.1515/tmj-2017-0008.
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