Numerical Investigation of the Steady State of a Driven Thin Film Equation

A third-order ordinary differential equationwith application in the flow of a thin liquid film is considered.The boundary conditions come from Tanner’s problem for the surface tension driven flow of a thin film. Symmetric and nonsymmetric finite difference schemes are implemented in order to obtain steady state solutions. We show that a central difference approximation to the third derivative in themodel equation produces a solution curvewith oscillations. Adifference schemebased on a combination of forward and backward differences produces a smooth accurate solution curve. The stability of these schemes is analysed through the use of a von Neumann stability analysis.