求解一类非线性方程的改进的平均法
A Modified Method of Averaging for Solving a Class of Nonlinear Equations
-
摘要: 本文研究确定非线性方程一致有效近似解的平均法,得到B方法(Krylov-Bogoliubov method)与KBM方法(Krylov-Bogoliubov-Mitropolski method)的改进形式,通过两个例子与多尺度方法的比较,说明改进的平均法的有效性,从而拓广了平均法的应用范围。Abstract: In this paper, we studied a method of averaging which decide a uniform valid solution for nonlinear equation and got the, modified forms for KB, method (Krylov-Bogoliubov method)and KBM method (Krytov-Bogoliubov-Mitropolski method). Through the comparison of two examples with the method of multiple scales it can be shown that the modifies averaging methods here are uniformly valid and there by the applied area of the method of averaging are extended.
-
Key words:
- KB method /
- KBM method /
- method of multiple scales /
- uniformlyvalid solution
-
[1] Nayfeh, A, H 《摄动方法导引》,宋家浦,戴世强译,上海翻译出版公司(1990). [2] Nayfeh, A, H 《摄动方法》,王辅俊等译,上海科学技术出版社(1984). [3] 戴世强,强非线性振子的渐近分析,应用数学和力学,6(5) (1985), 395-400. [4] 戴世强、庄峰青,一类非线性振动系统的渐近解,中国科学(A辑),(1) (1986), 34-40. [5] Nayfeh, A, H.,《振动方法习题集》,宋家啸、戴世强编译,上海翻译出版公司(1990). -
点击查看大图
计量
- 文章访问数: 1837
- HTML全文浏览量: 79
- PDF下载量: 476
- 被引次数: 0
下载:
