此外,从高阶平均方法,识别的外延k为订单的平均是其背后的目的是为了获得错误的估计O(εk)有效的时间。平均的另一种方法即平均周期系统慢时间依赖性获得了解了多个时间尺度。同样,平均吸引了平均的概念与景点获取解决方案,可用于方法精确和详细的解决方案。此外,周期平均和双曲率可以从不同的定理的描述,双曲线是常数对其结构(p.145 Antman et al .,2009)
In this dissertation, an effective and appropriate development of the asymptotic analysis of nonlinear dynamical system is presented through the use of different averaging differential methods. The diverse areas of literatures used within this study helped in presenting and understanding the underlying concepts along with the standard and definite solutions. Hence, it can be said that the aim of the study was thoroughly achieved by analyzing and investigating the different averaging methods of non-linear differential equations (Arrowsmith & Place, 1990, p.352). Moreover, the areas covered in this study, were distinct covering the quantitative and qualitative properties of the different averaging methods in a conceptual and theoretical way. Considering the different methods used in this study, the method of higher order periodic averaging helped in understanding the derivation and reduction of the Nth order value that are determined in a more strong and organized way.
Furthermore, from the higher-order averaging method, identification of the denotation of k for the averaging of the order was made as the purpose behind it was to gain estimation of the errors O (ε k) that are valid for time. Another method of averaging i.e. averaging periodic systems with slow time dependence helped in obtaining understanding about the multiple time scales. Likewise, averaging with attraction illustrated the concepts of averaging with attraction for obtaining the solution that can be used to approach an exact and detailed solution. Additionally, the periodic averaging and the hyperbolicity can be scrutinized from different theorems as it was depicted that the hyperbolic case is constant with respect to its structure (Antman et al., 2009, p.145)