, Volume 46, Issue 2, pp 313–323

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

Original Article

DOI: 10.1007/s11012-010-9310-3

Cite this article as:
Momoniat, E. Meccanica (2011) 46: 313. doi:10.1007/s11012-010-9310-3


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.


Thin filmThird-order ODEFinite differences0-stabilityVon Neumann stability

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