Phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution

A nonlinear third order singular ordinary differential equation is a model for a viscous fluid which drains over a wet surface as a thin film down a vertical wall. Here, we discuss the physical processes of a thin liquid film evolution. The classical thin film equation is being derived, and the series solution is obtained by employing the Adomian decomposition method (ADM). In this paper, a new way for the phase planes analysis and traveling wave solution by ADM is presented. The proposed algorithm is implemented using mathematical software Mathematica 6.0.