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

Abstract EN

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.