含小参数的波动方程初边值问题的渐近解
Asymptotic Solutions of Initial-Boundary Value Problems for Wave Equations with a Small Parameter
马乐 1刘树德1
作者信息
- 1. 安徽信息工程学院通识教育与外国语学院,安徽芜湖 241000
- 折叠
摘要
研究一类含小参数的波动方程的初边值问题,应用多尺度法构造它的一个近似解.通过在摄动展开式中引进不同的时间尺度,逐次消去出现在各阶展开式中的长期项,从而得出被认为是一致有效的渐近展开式.然后运用渐近展开理论给出上述一致有效性的严密性分析.所得结果表明:用一阶的一致有效展开式作为该问题的近似解,这与它的精确解相一致到O(ε2)阶.
Abstract
Some initial-boundary value problems for wave equations with a small parameter are studied.The problem whose approximate solution is constructed using the method of multiple scales.An as-ymptotic expansion is obtained,which is considered to be uniformly valid,by introducing different time scales in perturbed expansion and progressively eliminating secular terms from appearing in each order expansion.And then a precise analysis of the above uniformly validity is given using the theory of asymptotic expansion.The result is shown to regard a first order uniform expansion as an approxi-mate solution of this problem,in agreement with whose exact solution to O(ε2).
关键词
波动方程/初边值问题/渐近解/多尺度法/一致有效性Key words
wave equations/initial-boundary value problems/asymptotic solutions/the method of mul-tiple scales/Uniformly validity引用本文复制引用
基金项目
安徽省高等学校科学研究重点项目(2023AH052921)
2022年度安徽省省级质量工程项目(2022jyxm682)
出版年
2024
NETL
NSTL
万方数据