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

Manoj Kumar
Neelima Singh
Journal / Anthology

Computers and Mathematics with Applications
Year: 2012
Volume: 64
Page range: 28862895

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 byADMis presented. The proposed algorithm is implemented using mathematical software Mathematica 6.0.

*Applied Mathematics

Third order singular problems, Thin film flows, Adomian decomposition method, Phase plane, Contact line, Pade approximants