Asymptotic Solution for Model with Small Parameter

Model with small parameter is considered. Such problem undergo rapid changes within the boundary layer since the presence of the small parameter. Firstly, the analytical result of the problem is studied. The bound of the analytical solution is presented by Gronwall inequality. Secondly, the analytical solution is decomposed into the computational component and the small component. It is proved to be uniformly bound with respect to the small parameter in order one for the small component. Finally, numerical experiment is given to support the theoretical result.