Numerical Investigation of the Steady State of a Driven Thin Film Equation
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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.
Analytical and numerical
results on the positivity of steady state solutions of a thin film
equation
2013 ◽
Vol 18
(5)
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pp. 1305-1321
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2016 ◽
Vol 261
(2)
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pp. 1622-1635
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2008 ◽
Vol 245
(6)
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pp. 1454-1506
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1970 ◽
Vol 28
◽
pp. 544-545
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