Analytic Solution for a Nonlinear Problem of Magneto-Thermoelasticity

In this paper, we present a comparative study of the homotopy analysis method (HAM), the variational iteration method (VIM) and the iterative method (Heʹs polynomials). The approximate solution of the coupled harmonic waves nonlinear magneto-thermoelasticity equations under influence of rotation is obtained. In order to control and adjust the convergence region and the rate of solution series, we show that it is possible to choose a valid auxiliary parameter h of HAM. Using the boundary and the initial conditions we select a suitable initial approximation. The results show that these methods are very efficient, convenient and applicable to a large class of problems.