The behavior of an evaporating thin film of a highly wetting liquid filled in a rectangular groove was studied theoretically. Following the previous studies, the liquid film was divided into an adsorbed film region, a micro region and an intrinsic meniscus region. A theoretically based method was employed to estimate the Hamaker constant. The Marangoni effect due to the thickness change of a very thin liquid film was included in the basic equation. The fourth order differential equation for the liquid film thickness was solved by the finite difference method. Three sets of the combination of boundary conditions at both ends of the micro region were examined and the set of boundary conditions which gave the most realistic solution was decided. The solutions were obtained for a wide range of the micro region length. The principle of maximum entropy production was introduced to estimate the most probable solution. The results were compared with previous results obtained by the shooting method and the effect of the solution method on the numerical results was discussed. (C) 2014 Elsevier Ltd. All rights reserved.