Ordinary differential equation with periodical boundary value and small parameter multiplied in the highest derivative was considered. The solution of the problem has boundary layers, which is thin region in the neighborhood of the boundary of the domain. Firstly, the properties of boundary layer were discussed. The solution was decomposed into the smooth component and the singular component. The derivatives of the smooth component and the singular component were estimated. Secondly, mesh partition techniques were presented according to one transition point method and multi-transition points method. Thirdly numerical methods based on non-equidistant mesh partition were presented to solve the problem. Finally error estimations were given for both computational methods.