Numerical investigation of the steady state of a driven thin film equation

A third-order ordinary differential equation with 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 the model equation produces a solution curve with oscillations. a difference scheme based 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. © 2013 a. j. hutchinson et al.