Assessment of two analytical approaches in some nonlinear problems arising in engineering sciences

In this research, two powerful analytical methods are introduced to handle nonlinear good Boussinesq, heat transfer and coupled Burgers' equations. One is the homotopy-perturbation method (HPM) and the other is the variational iteration method (VIM). VIM is used to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory. HPM converts a difficult problem into a simple one, which can be easily handled. The results attained in this paper confirm the idea that HPM and VIM are powerful mathematical tools and that they can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.