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来源：百度知道 编辑：UC知道 时间：2024/05/26 10:51:18
分离变量法就是通过变量分离的方法将偏微分方程化为变量更少的偏微分方程，或者是常微分方程。分离变量法的精神其实就是将未知函数分开，例如，如，令
U(x,y,z;t) = X(x)Y(y)Z(z)T(t)
从而，将偏微分方程的求解问题，化为若干个常微分方程的定解问题来求解。
这实际上也是一种化归方法。它适用于波动方程问题、运输问题和稳定场问题在特殊域（矩形、长方形、圆、圆球，圆柱体等）的定解问题，因为这些特殊域正好常常在实际问题中出现，因而分离变量法有着广泛的应用。分离变量法的化归思想就是试着构造一个给定偏微分方程的解u，通过分离变量法使得函数所含的变量减少，从而便于求解。换句话说，分离变量法就是假定u能写成一些未定的函数（含有少量变量）的和或积的组合，将其代入原来的偏微分方程，然后找出那些函数使得u是方程的一个解。
The separation variable method will be is partial to the differentialequation through the variable separation method to change into thevariable less deviations differential equation, or will be theordinary differential equation. The separation variable method spiritactually is separates the unknown function, for example, like,command U (x, y, z; T) = X (x) Y (y) Z (z) T (t) Thus, will be partial to the differential equation the solutionquestion, will change into certain the ordinary differential equationto decide the solution question to solve. This also is one plan method in fact. It is suitable for the waveequation question, the transportation question and the stabilizingfield question in the special territory (rectangle, rectangle, circle,sphere, circular cylinder and so on) decides the solution question,because these special territories happen to frequently appear in theactual problem, thus the separation variable method has the widespreadapplication. The separation variable met