In this chapter, the homotopy perturbation and Adomain's
decomposition methods are applied to obtain the approximate solutions of the
equation of motion and heat equation for the harmonic waves propagation in a
nonlinear generalized thermoelasticity with magnetic field. The nonlinear
coupled system of partial differential equations often appear in the study of
circled fuel reactor, high-temperature hydrodynamics and thermo-elasticity
problems. The problem is solved in one-dimensional elastic half-space model
subjected initially to a prescribed harmonic displacement and the temperature
of the medium. The displacement and temperature are calculated for the two
methods with the variations of the magnetic field and the relaxation times
considering Green Lindsay theory (GL). The results obtained are displayed
graphically to show the in uences of the new parameters and the differs between
the methods technique. It is obvious that the homotopy perturbation method and
adomain decomposition method give the same results that indicates to the origin
of the approximate solutions and the methods powerful. The homotopy
perturbation method and adomain decomposition method give the same results that
indicates to the origin of the approximate solutions and the methods powerful.
Author(s) Details
S. M. Abo-Dahab
Mathematics Department, Faculty of Science, South Valley University, Qena
83523, Egypt.
Khaled A. Gepreel
Department of Math, Faculty of Science, Taif University, Saudi Arabia and
Department of Math, Faculty of Science, Zagazig University, Egypt.
Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v1/1034
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