**6.1 Solution methodology: Galerkin decomposition and homotopy perturbation methods**

The method of solution for the governing equation includes Galerkin decomposition and homotopy perturbation methods. As the name implies the Galerkin decomposition method is used to decompose the governing partial differential equation of motion can be separated into spatial and temporal parts. The resulting temporal equations are solved using homotopy perturbation method.

The procedures for the analysis of the equations are given in the proceeding sections as follows:
