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

A. J. Hutchinson, C. Harley and E. Momoniat

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/181939

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:181939

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