Open Access
2013 Numerical Investigation of the Steady State of a Driven Thin Film Equation
A. J. Hutchinson, C. Harley, E. Momoniat
J. Appl. Math. 2013(SI27): 1-6 (2013). DOI: 10.1155/2013/181939


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.


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A. J. Hutchinson. C. Harley. E. Momoniat. "Numerical Investigation of the Steady State of a Driven Thin Film Equation." J. Appl. Math. 2013 (SI27) 1 - 6, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.76009
MathSciNet: MR3032204
Digital Object Identifier: 10.1155/2013/181939

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI27 • 2013
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