Numerical simulation method for periodical model

Periodical problem is of common occurrence in many applied fields. In this paper the equation with periodical condition and small parameter is considered. The problem will lead to large oscillation since the parameter is small. The boundary layer function is presented firstly. The smooth component is constructed by the boundary layer function secondly. The error estimation of analytical solution is proved to be order one with respect to small parameter thirdly. Finite differential method is proposed for the smooth component. Numerical error analysis is given fourthly. Simulation example is presented to illustrate our theoretical result finally.