Abstract
The homotopy perturbation method and variational iteration method are applied to obtain the approximate solution of the harmonic waves propagation in a nonlinear magneto‐thermoelasticity under influence of rotation. 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 methods with the variations of the magnetic field and the rotation. The results obtained are displayed graphically to show the influences of the new parameters and the difference between the methods′ technique. It is obvious that the homotopy perturbation method is more effective and powerful than the variational iteration method.
Highlights
In the past recent years, much attentions have been devoted to simulate some real-life problems which can be described by nonlinear coupled differential equations using reliable and more efficient methods
The nonlinear coupled system of partial differential equations often appear in the study of circled fuel reactor, high-temperature hydrodynamics, and thermoelasticity problems, see 1–4
Wave generation in nonlinear thermoelasticity problems has gained a considerable interest for its utilitarian aspects in understanding the nature of interaction between the elastic and thermal fields as well as for its applications
Summary
In the past recent years, much attentions have been devoted to simulate some real-life problems which can be described by nonlinear coupled differential equations using reliable and more efficient methods. The nonlinear coupled system of partial differential equations often appear in the study of circled fuel reactor, high-temperature hydrodynamics, and thermoelasticity problems, see 1–4. Much attention has been devoted to numerical methods, which do not require discretization of space-time variables or linearization of the nonlinear equations, among which the variational iteration method VIM suggested in 8–20 shows its remarkable merits over others. The method was successfully applied to a nonlinear one dimensional coupled equations in thermoelasticity 21 , revealing that the method is very convenient, efficient, and accurate. Applying He’s variational iteration method for solving differential-difference equation is discussed by Yildirim. Mohyud-Din and Noor 29, used Homotopy perturbation method for solving some new boundary value problems. The homotopy perturbation method and variational iteration method are used to solve the coupled harmonic waves nonlinear magneto-thermoelasticity equations under influence of rotation. The displacement and temperature which obtained have been calculated numerically and presented graphically
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