| 完全近似法的推广及其应用* |
| |
| 引用本文： | 戴世强. 完全近似法的推广及其应用*[J]. 应用数学和力学, 1991, 12(3): 237-244 |
| |
| 作者姓名： | 戴世强 |
| |
| 作者单位： | 上海工业大学, 上海市应用数学和力学研究所 |
| |
| 基金项目： | 国家自然科学基金，上海市自然科学基金 |
| |
| 摘 要： | 本文提出完全近似法的一种推广形式:引用渐近线性化的概念,通过对坐标作包含因变量的非线性泛函的变换,把原有的非线性问题线性化,从而以首项渐近解和相应的坐标变换给出原问题的较高阶的近似解析解.对模型方程和若干弱非线性振动和波动问题的分析表明,本文提出的方法是简捷而有效的.
|
| 关 键 词： | 摄动法 完全近似法 渐近线性化 非线性波 非线性振动 |
| 收稿时间： | 1990-05-09 |
Generalization of the Method of Full Approximation and Its Applications |
| |
| Dai Shi-qiang. Generalization of the Method of Full Approximation and Its Applications[J]. Applied Mathematics and Mechanics, 1991, 12(3): 237-244 |
| |
| Authors: | Dai Shi-qiang |
| |
| Affiliation: | Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University of Technology, Shanghai |
| |
| Abstract: | This paper presents a generalized form of the method of full approximation. By using the concept of asymptotic linearization and making the coordinate transformations including the nonlinear functionals of dependent variables, the original nonlinear problems are linearized and their higher-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations. The analysis of a model equation and some problems of weakly nonlinear oscillations and waves with the geneialized method shows that it is effective and straightforward. |
| |
| Keywords: | perturbation methods methods of full approximation asymptotic linearization nonlinear -waves nonlinear oscillations |
| 本文献已被 CNKI 维普 等数据库收录！ |
| 点击此处可从《应用数学和力学》浏览原始摘要信息 |
|
点击此处可从《应用数学和力学》下载全文 |
