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Numerical investigation of a third-order ODE from thin film flow

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Abstract

We compare two finite difference schemes to solve the third-order ordinary differential equation y'''=y −k from thin film flow. The boundary conditions come from Tanner’s problem for the surface tension driven flow of a thin film. 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. Both the 0-stability and von Neumann stability properties of the different finite difference schemes are analyzed. The solution curves obtained from both approaches are presented and discussed.

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  1. Centre for Differential Equations, Continuum Mechanics and Applications School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits, 2050, South Africa

    E. Momoniat

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Momoniat, E. Numerical investigation of a third-order ODE from thin film flow. Meccanica 46, 313–323 (2011). https://doi.org/10.1007/s11012-010-9310-3

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