Aims and objective: The existence of unique, qualitative, and quantitative mathematical techniques for averaging the differential equations that are not linear are significantly important in mathematical field. The study aims to analyze the different averaging methods of non-linear differential equation.
Methodology: The averaging methods such as higher order periodic averaging, averaging periodic systems with slow time dependence, second-order averaging, periodic averaging and hyperbolicity, Hamiltonian normal form theory, averaging with attraction, and averaging over angles are used in the study. These methods are evaluated using the content analysis technique because through this method, the reasonable mathematical analysis to build or select a numerical method can be obtained.
Results and Findings: The results and findings of the study reveal that these methods can be used to select the most suitable numerical method and can be used to build another numerical method. The graphs are plotted through Maple for analyzing non-linear differential equations.