變數分離（法）；變量分離（法）
The method of separation of variables and the method of eigenfunction expansion are used to derive the calculation equations of stress singularities at crack tip.
利用分離變量法及本征函數向量展開等方法，推導出裂紋尖端的應力奇性解的計算公式。
The Schrdinger equation is given directly from the classical Hamiltonian function of a damping harmonic oscillator, and its solution is obtained by the separation of variables.
寫出阻尼諧振子的哈密頓函數，對其直接量子化，用分離變量法得出了薛定谔方程的解。
The Green's functions for electric and magnetic vector potentials in a sectoral wave guide and its cavity are derivated by using the separation of variables, Fourier transform and residue theory.
文中介紹了扇面直波導及其腔體中電矢量位和磁矢量位的格林函數，采用分離變量法、傅裡葉變換法和留數定理導出了格林函數的具體表達式。
By using separation of variables and double Fourier series, we obtain a solution to the initial-boundary value problem of the forced vibration of this rectangular membrane.
利用分離變量法和二重傅裡葉級數的方法，得到了矩形膜的受迫振動初邊值問題的解。
Firstly, the expressions of free vibration of moderately thick plates in polar coordinates are derived and the general solutions are obtained by the means of method of separation of variables.
首先，導出了用極坐标系描述的中厚闆自由振動闆的微分方程，用分離變量法求得其一般解。
Separation of variables is employed to solve the differential equation under the boundary condition of two ends of the girder being simply supported, and the solution of stress is…
在兩端簡支的邊界條件下采用分離變量法求解偏微分方程，得到用級數表示的應力解，然後根據剪力滞系數的定義即可得到組合箱梁翼闆的剪力滞系數。
The lateral displacement of lattice shell is obtained by separation of variables for fixed boundary condition.
闆殼承受橫向載荷，除了有面内位移外，還存在面外位移。
We derive the analytic solution of the non-homogeneous fractional diffusion-wave equation under the mixed boundary conditions using the method of separation of variables.
利用分離變量方法導出了在混合邊界條件下的非齊次分數階擴散-波動方程的解析解。
Separation of variables method for fractional diffusion-wave equation with initial-boundary value problem in three dimensions;
讨論一類在部分區域上的奇攝動反應擴散方程初始邊值問題。
In the paper, the dynamic axial response of bar during impact, while the impactor and target are regarded as a system of vibration, is analyzed by means of variables separation method.
本文采用模态分析方法，分析了任意支承條件下杆的沖擊動力響應。
The separation on a shaking table is controlled by a number of operating variables and the importance of these variables in the model development is described.
讨論了控制搖床選别的操作變量及這些變量在模型研究中的重要性。
By using variables separation in the complex number field, the real analytical solution in the form of Fourier series was obtained.
在複數域内利用分離變量法，得到了這類方程的級數形式的解析解，而最後的解是實數形式。
Based on pickling principle, research results of membrane separation process and experience of engineering practice, the author developed a method of solving equations in multiple variables.
作者根據鋼鐵酸洗原理、膜分離工藝研究結果和工程實踐經驗，提出了多元一次方程求解法。
In the chapter 2, we find the separation of variables solutions for nonlinear reaction diffusion equation (2.4) by utilizing the group foliation method.
在第二章中我們主要利用群分支法來求解非線性擴散方程（2.4）的分離變量解。
The temperature field around a straight buried pipe was analyzed using conformal mapping, separation of variables and boundary discretization. A series solution was obtained for the temperature field.
為了對直埋管道保溫層及其土壤鄰域的溫度場進行較精确的分析，采用保形映射、分離變量和邊界離散法對地下直埋管道的溫度場進行分析，得到了級數形式的解。
When the flow is a supersonic one, separation of variables will be used for a square experimental section.
在超音速流時，對矩形實驗段區域，則采用分離變數法求解。
After some reasonable assumption and simplicity, a two-dimensional analysis method has been got with separation of variables.
本文通過一系列合理假設和簡化後，利用分離變量法，推導出計算汽缸溫度場的二維解析法。
Third, the mode solution is obtained using the separation of variables. The last, the mode transition property is discussed when the plane wave transmit in the step-index optical fiber.
再次，利用分離變量法推導出平面波在階躍光纖中傳播的模式表達式，讨論了光波在光纖中傳播的模式特性。
Separation of variables is one basic method of boundary value problems.
分離變量法是解邊值問題的一種基本方法。
分離變量法（Separation of Variables）是一種求解偏微分方程的數學方法，尤其適用于具有特定對稱性的物理問題（如直角、柱面或球坐标系下的波動方程、熱傳導方程等）。其核心思想是将多變量函數分解為單變量函數的乘積，從而将原方程轉化為多個常微分方程分别求解。
假設解的形式為多個單變量函數的乘積。例如，對于二元函數 ( u(x,t) )，假設解為： $$ u(x,t) = X(x)T(t) $$ 将這一形式代入原偏微分方程，通過代數操作将方程分離為僅含單一變量的部分，使得兩邊等于同一常數（通常記為 (-lambda)），從而得到獨立的常微分方程。
該方法通過降維簡化了問題，但需注意其適用範圍。對于更複雜的情況，可能需要結合其他方法（如積分變換或數值計算）。
分離變量法（Separation of Variables）是數學中的一種求解偏微分方程的方法。它主要應用于求解偏微分方程中的邊值問題。該方法的核心思想是将多元函數表示為單元函數的乘積形式，然後對單元函數分别進行求解。
用法
分離變量法適用于一類偏微分方程，即可以表示為各個變量的函數相乘的形式。通常情況下，該方法用于求解定解問題。在求解過程中，需要将偏微分方程中的未知函數表示為各個變量的乘積形式，然後将各個變量分别進行求解。
例句
英文：The separation of variables method is a powerful technique for solving partial differential equations.中文：分離變量法是求解偏微分方程的一種強大的技術。
英文：The separation of variables method can be used to solve various types of partial differential equations.中文：分離變量法可以用于解決各種類型的偏微分方程。
解釋
分離變量法是一種求解偏微分方程的方法，其基本思想是将多元函數表示為單元函數的乘積形式，然後對單元函數分别進行求解。該方法可以用于求解一定範圍内的偏微分方程邊值問題。
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