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