强非线性微分方程符号分析法的计算机实现及有效性研究  

A Study on the Effectiveness and Computer Realization of Symbolic Analysis for Strongly Nonlinear Differential Equations

作　　者：宁送云[1] 丘水生[2] 

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

出　　处：《广东教育学院学报》2006年第3期45-48,共4页Journal of Guangdong Education Institute

摘　　要：目前国际上正在寻找一种分析强非线性系统的方法,而等效小参量法目前在文献中可查到的应用仅限于失真度小于20%以下的系统.文章对等效小参量法的原理进行分析,认为该方法可以适用于更强的非线性系统分析.在此基础上,使用Matlab语言编程,用符号迭代法求解出一个典型强非线性系统方程的近似解,并用数值分析验证其结果的有效性和准确程度.分析结果表明,等效小参量法能够适用于失真度大于25%以上的系统,满足目前国际上的实际需要.To find a new general method for analyzing strongly nonlinear system is an international task at present. However, the applications of the Equivalent Small Parameter（ESP） method in the existing literature are restricted to systems whose distortion（HD） is less than 20%. The thesis analyzes the ESP method, and the conclusion is that it is suitable for analyzing strongly nonlinear systems. Based on this, a classic strongly nonlinear equation is studied with Matlab program, at the same time, the effectiveness and accuracy of the method are verified by numerical analysis. The results show that the method is suitable for systems with distortion above 25 % and it meets the international requisition.

关 键 词：等效小参量法 强非线性 符号迭代 近似解析解 数值分析 

分 类 号：TM132[电气工程—电工理论与新技术]