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In this work we use the lubrication type method, based on the possibility of the separation of longitudinal and transversal length scales, to simplify the analysis of coating film dynamics. We study the dynamics of coating thin films on horizontal stationary and rotating cylinders in general, and when the effect of van der Waals forces is significant. A computer code based on the method of orthogonal collocation is developed and is used for the study of the instabilities of coating thin film flow on cylinders to identify conditions of stable operation. For stationary cylinders, the equations are symmetric and the two spline collocation second-order formulation method is most appropriate. For rotating cylinders, a spline collocation first-order formulation method is most efficient.As expected in all cases positive van der Waals forces cause rupture of the film with the rupture time of the film decreasing with the increase of van der Waals forces. Gravity, on the other hand, has a stabilizing effect and increases rupture time.