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**Numerical investigation of the steady state of a driven thin film equation.**
*(English)*
Zbl 1266.76009

Summary: 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.

### MSC:

76A20 | Thin fluid films |

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\textit{A. J. Hutchinson} et al., J. Appl. Math. 2013, Article ID 181939, 6 p. (2013; Zbl 1266.76009)

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### References:

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