D’Alembert方法通常应用于无限长弦自由振动初值问题的求解，基于这种思想研究带有Neumann边界波动方程初边值问题的达朗贝尔类精确解。对于有限长区间上的波动方程初边值问题，通常采用分离变量法求解。现用适当的延拓方法：一种是直接通过逐次延拓时间 ，获得有限长区间带有Neumann边界的波动方程初边值问题按时间分段表示的解；另一种方法是通过对初始位移和速度的定义域进行延拓，获得有限长区间带有Neumann边界的波动方程初边值问题的D’Alembert类解。
Abstract
D’Alembert method usually is applied in solving the initial problem of an infinite-long string free vibration.Based on the idea of this method, D’Alembert analytical solution to initial-boundary value problems of wave equation with Neumann boundary was studied.For initial-boundary value problems of wave equation within a finite long time interval, the method of variable separation was usually adopted to solve them.Two kinds of the continuation methods were used to solve these problems.One kind was that through successively extending time t, the time piecewise solution to an initial-boundary value problem of wave equation with Neumann boundary was derived within a finite long time interval.Another was that through extending definition fields of the initial displacement and initial velocity, D’Alembert type solution to an initial-boundary value problem of wave equation with Neumann boundary was derived within a finite long time interval.
关键词
波动方程 Neumann边界 D&rsquo /
Alembert 行波解
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Key words
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Wave equation Neumann boundary D&rsquo /
Alembert Traveling solutions
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