弱非线性系统＋ω_0~2=εf（t,x,）近似解的求解  

Solving of Weakly Nonlinear System's Approximate Solution

作　　者：吕堂红[1] 周林华[1] 

机构地区：[1]长春理工大学理学院,长春130022

出　　处：《长春理工大学学报（自然科学版）》2010年第3期166-170,共5页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金(10571073)

摘　　要：本文首先介绍了常数变易法和平均法的发展历程,其次研究了求解弱非线性系统+ω_0～2=εf(t,x,)近似解的平均法及其与常数变易法的关系,以及平均法的原理,最后给出算例,验证了平均法是求解弱非线性系统+ω_0～2=εf(t,x,)近似解的有效方法。In this paper, firstly, we introduce the development history of constant variation method and averraging method. Then, we study the averaging method and its relationship with the constant variation method m solving the weakly nonlinear system x＋ω^22x=Rf（t,x,x）. Eventually, we give an example, which illustrates tile effectiveness of the averaging method.

关 键 词：常数变易法 平均法 非齐次常微分方程 

分 类 号：O175[理学—数学]