Abstract: Renormalization Group (RG) method is a general method whose aim is to globally approximate solutions to differential equations involving a small parameter.In this thesis, we will give an algorithm for the RG method to generate the RG equation needed in the process of finding an approximate solution for ODEs.In chapter 1, we have some introduction to perturbation theory and introducing some traditional methods in perturbation theory.In chapter 2 we compare the results of RG and other