一个非线性波动方程的计算机代数-摄动解<sup>*</sup>

一个非线性波动方程的计算机代数-摄动解^*

基金项目: * 国家自然科学基金和上海市自然科学基金

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China

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。
- 非线性波动 /
- 摄动 /
- 计算机代数 /
- 重整化法 /
- 近似解析特征线法
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).
- nonlinear wave /
- perturbation /
- computer algebra /
- renormalization technique /
- approximate analytical method of characteristics

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