Coupled system of two second order ordinary differential equations with small parameter was considered. This is a multi-scale system. The solution of the system will change rapidly near both sides of the boundary layer. The system was decomposed into several systems in order to have fourth order asymptotic decomposition firstly. The asymptotic properties of all these systems were discussed secondly. The third order numerical methods were constructed for left side and right side singular component systems thirdly. The error estimation for the system was given finally.