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.
目的：独特的，定性的存在，和平均是不是线性的微分方程数学定量技术在数学领域的重要。本研究旨在分析不同的平均方法的非线性微分方程。
方法：取平均的方法如高阶周期平均，平均周期系统缓慢的时间依赖性，二阶平均，周期平均和双曲正规形理论，哈密顿量，平均有吸引力，和平均的角度研究中使用。使用这些方法进行评估的内容分析技术，通过这种方法，合理的数学分析，建立或选择一个数值方法可以得到。
结果：结果和研究结果表明，这些方法可以用来选择最合适的数值方法可用于构建一个数值方法。图形绘制通过枫分析非线性微分方程。
