Semi-analytical method for propagation of harmonic waves in nonlinear magneto-thermo-elasticity

In this paper, we develop and apply a semi-analytical method called the Method of Directly Defining inverse Mapping (MDDiM) to obtain a series solution for the propagation of harmonic waves in a nonlinear generalized thermo-elasticity with relaxation time, heating, rotation, and magnetic field. We obtained third order approximate solutions for the displacement and the temperature fields of the waves with variations in the magnetic field, the relaxation time, and the rotation. The obtained results, with minimum errors, are presented graphically and discussed. Our new extended MDDiM out performs the existing Optimal Homotopy Analysis Method (OHAM) with minimum error and a faster convergent rate. The method can be applied to various systems of nonlinear partial differential equations arising in science and engineering.

Automated summary

In this paper, a semi-analytical method called MDDiM is developed and applied to solve the problem of harmonic wave propagation in nonlinear generalized thermo-elasticity. By varying the magnetic field, relaxation time, and rotation, approximate solutions for the displacement and temperature fields are obtained and presented graphically. The new extended MDDiM method outperforms the existing OHAM with minimum error and faster convergence rate.