Application of He's homotopy perturbation and He's variational iteration methods for solution of Benney–Lin equation

In this paper, we study the Benney–Lin equation using He's homotopy perturbation method (HPM) and He's variational iteration method (VIM). We compare HPM and VIM methods and show that the results of the HPM method are in excellent agreement with the results of the VIM method and the obtained solutions are shown graphically. Several cases are considered to apply HPM and VIM, which demonstrate the reliability and efficiency of these two methods in solving such a complicated equation with various initial conditions.