Higher-order periodic averages are also one of the methods of calculating the periodic averages for the nonlinear equations. These higher order averages are determined by the structuring of the lower order averages in a more organized and structured way. It has been depicted from the work of the Ellison et al. cited in Trigg, (2006, p.396) that chose and took the basic algorithm and created an improved Nth order estimation to extend the theory of the higher-order averaging in order to demonstrate the manner of averaging theory that might be used for proving the continuation of overall course of time-dependent differential equations (Trigg, 2006, p.396). In higher-order averaging, k denotes the averaging of the order with the purpose to gain estimation of the errors ( k) that are valid for time (Sanders et al., 2007, p.43).
Moreover, in order to simplify the assumptions of all the functions of periodic averaging, these are demonstrated on Rn, on the other hand helping in proving the near-identity transformations (Sanders et al., 2007, p.38).
高阶周期平均值也是一个用于计算非线性方程的周期平均值的方法。这些高阶平均值是有组织的和结构化的方式由低阶的平均结构的确定。它被描述的埃里森等人的工作。引用在特里格，（2006，p.396），选择了基本算法和创造了一个改进的N阶估计将高阶平均为说明平均理论可以用来证明随时间变化的微分方程的全过程的延续方式的理论（特里格，2006，p.396）。在高阶平均，k表示的平均订单以增益的误差的估计（εK），有效时间（Sanders等人。，2007，第43页）
此外，为了简化周期平均的所有功能的假设，这表明在Rn，另一方面帮助证明近身份的转换（Sanders等人。，2007，p.38）。
