一个非线性波动方程的计算机代数-摄动解*
Computer Algebra-Perturbation Solution to a Nonlinear Wave Equation
-
摘要: 本文采用计算机代数-摄动法讨论一个非线性波动方程的Caychy问题高阶渐近解,将特征坐标变形与重整化方法相结合,消除直接展开解的长期项,并利用计算机代数软件进行符号运算,得到该问题的四项摄动解,所得的渐近解与数值解的比较表明:对较小的ε,两者相吻合;对较大的ε(如ε=0.25),两者也相当符合。Abstract: In this paper, the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a computer algebra-perturbation method. The secular terms in the solution from straightforward expansions, are eliminated with the straining of characteristic coordinates and the use of the renormalization technique, and the four-term uniformly valid solution is obtained with the symbolic computation by using a computer algebra system. The comparison of the derived asymptotic solution dnd the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger ε(e. g., e=0.25).
-
[1] 钱伟长主编,《奇异摄动理论及其在力学中的应用》,科学出版社,北京(1981). [2] Nayfeh,A.H,,An Introduction to perurbation Techniques,John Wiley & Sone,New York(1981).中译本:《摄动方法导引》(宋家骕译).上海翻译出版公司(1990). [3] Kevorkian,J,and J,D,Cole,Pertuibation Methods in Applied Mathematics,Springer-Yerlag,New York(1980). [4] Rand,R.H.and H.Armbruster,Perturbation Methods,Bifurcation Theory and Computer Algebra,Springer-Yerlag,New York(1987). [5] 藏宏鸣,若干力学问题的摄动-计算机代数研究,上海工业大学硕士学位论文(1993). [6] 衷仁保,《计算机代数》,国防科技大学出版社,长沙(1989). [7] 藏宏鸣、戴世强,一个非线性摄动方程的计算机代数解,上海工业大学学报,14(3)(1993),189-197. [8] 王明祺、戴世强,Duffng方程摄动解的计算机延伸,上海工业大学学报,15(4)(1994). [9] Zang Hong-ming and Dai Shi-qiang,Higher-order solutions for interfacial,solitary waves in a two-fluid system,Porc,Int,Conf,on Hydrodyn.,Ocean Press,Beijivg(1994). [10] van Dyke,M,,Computer-extended series,Ann.Rev,Fluid Mech.,16(1984),287-309. [11] 戴世强,PLK方法,见[1],33-86. -
点击查看大图
计量
- 文章访问数: 2323
- HTML全文浏览量: 136
- PDF下载量: 577
- 被引次数: 0
下载:
