Meccanica

, Volume 46, Issue 2, pp 313–323

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

Original Article

Abstract

We compare two finite difference schemes to solve the third-order ordinary differential equation y'''=yk 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.

Keywords

Thin film Third-order ODE Finite differences 0-stability Von Neumann stability 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Centre for Differential Equations, Continuum Mechanics and Applications School of Computational and Applied MathematicsUniversity of the WitwatersrandWitsSouth Africa

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