Uniform convergence method for model with small parameter and Robin boundary condition

Model with small parameter and Robin boundary condition is considered. This is a multi-scale problem. The presence of small parameter leads to boundary layer phenomena. In order to discrete robin boundary condition and improve the order of uniform convergence, first transition point, which is very small, is introduced firstly. The domain is divided into the inner boundary layer region and the outside boundary layer region according to second transition point secondly. The new method is proved to be stable and high order uniformly convergent with respect to small parameter finally.