等效小参量法求解强非线性系统的有效性研究  

Study on Effectiveness of the Equavalent Small Parameters Method for Solving the Strongly Nonlinear Systems

作　　者：宁送云[1] 丘水生[2] 

机构地区：[1]广东药学院基础学院,广州510006 [2]华南理工大学电信学院,广州510641

出　　处：《中原工学院学报》2007年第4期39-43,共5页Journal of Zhongyuan University of Technology

摘　　要：文章在已有研究的基础上,通过对不同失真度的非线性系统进行求解和比较,得出结论:等效小参量法对于失真度达到30%左右的非线性系统分析是有效的.同经典的扰动法相比较,在非线性较弱时,等效小参量法和扰动法一样能获得精确的结果,但是,在非线性较强时,等效小参量法表现出比较明显的优势.Of all the symbolic analysis methods for solving strongly nonlinear differential equations, the effectiveness and applicability of the ESP（Equavalent Small Parameters） method is good enough. However, it＇s application is restricted to the systems whose distortion is less than 20%. Based on the results above, several nonlinear systems with different distortion are studied and compared,the conclusion is that it is suit for analyzing nonlinear systems with distortion up to 30 %. Compared with the classic perturbation method, both can obtain accurate results for weakly nonlinear systems, while for strongly nonlinear systems, the ESP method has obvious advantages.

关 键 词：等效小参量法 强非线性 近似解析解 数值分析 扰动法 

分 类 号：TM132[电气工程—电工理论与新技术]