摘要
本文应用同伦技术和摄动技术,提出了一种新的摄动思想。这种方法有别于传统的摄动理论,它不依赖于小参数,而是应用同伦技术,构造一个含嵌入参数p∈[0,1]的方程,然后把嵌入参数作为“小参数”,因此这种新方法可以克服传统摄动理论的不足,而又可充分应用各种摄动方法。其结果显示这种方法简单而有效,并且其一阶近似往往具有很高的精度。
In this paper, it presents a coupling method, the combination of homotopy technique and perturbation technique to solve nonlinear problems. In contrast to the traditional perturbation methods, the proposed method does not require small parameter in the solution of a nonlinear differential equation. In this method, according to the homotopy technique, a homotopy with an imbedding parameter p∈ [0,1] is considered as 'small parameter', so the proposed method can overcome the disadvantages and limitations of the traditional perturbation methods. Results of solutions reveal that the new method is very effective and simple, and it appears that even the first-order solution is of good accuracy.
出处
《上海力学》
CSCD
1999年第1期56-63,共8页
Chinese Quarterly Mechanics
基金
上海市高等学校青年科学基金(98QN47)
关键词
非线性振动
摄动理论
同伦技术
摄动参数
nonlinearity, nonlinear oscillation, perturbation method, homotopy.
