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SUMMARY In this paper, the nonlinear third‐order singular ordinary differential equations that arise in draining and coating flows are studied and computationally solved by employing the modified Adomian decomposition method, and the series solutions of the governing nonlinear problems are developed. Because of singularity, it is not possible to move a contact line over a no‐slip surface, so we cannot find the solution of such problems. To overcome this difficulty, we modify boundary condition to apply the modified Adomian decomposition method with Padé approximants. Copyright © 2011 John Wiley & Sons, Ltd.