The methods of research are numerical analysis and approximate analytic solution.
研究方法有数值法和近似解两种。
Comparison of numeric results with analytic solution showed the effectiveness of the method.
数值结果同解析解进行了对比，表明了本方法的有效性。
This method is helpful for us to find the way of the analytic solution of scalar field equation.
他们的解析解法对我们寻求标量场方程的解析解有着重要的启发意义。
Taking account of the influence of coolant, an analytic solution is given for grinding temperature.
在解析磨削温度时，考虑了冷却液的影响。
This paper presents in brief the fundamental way of analytic solution by Finite Analytic Method (FAM).
本文简要介绍有限解析法（FAM）的基本解题思路。
Because of the use of Green - function method to solve local analytic solution, its accuracy is increased.
由于使用格林函数法求局部解析解，提高了计算精度。
The analytic solution describing the spatial period was obtained and it is accordant with experimental result.
求出了空间周期解析解的表达式，此结果与实验结果相符。
Finally, the analytic solution is compared with numerical one, both are in very good agreement with each other.
解析解与数值解进行了比较，两者取得了很好的一致。
The analytic solution is important to predict the reliability of micro inertial sensors worked in shock environment.
此冲击响应解析解对预测微惯性传感器在冲击环境下的可靠性具有重要作用。
Using finite analytic solution we gave the numerical computation of the flow field in CVD reactor with tilted susceptor.
本文用有限分析方法，对带有倾斜基座的CVD反应器内流场进行了数值计算。
Discussed the existence and uniqueness of the analytic solution of the atmospheric circulation equations' mixed problem.
大气环流方程组混合问题解的存在唯一性讨论。
This static cable element stiffness matrix has a high accuracy since it comes from the analytic solution of a parabolic cable.
该静刚度矩阵来自抛物线索的解析解，具有很高的精度，明显比悬链线索单元简化了许多。
So we use an analytic solution algorithm to solve the three-temperature energy equation, which makes the calculation much simpler.
所以我们采用了一种求解析解的算法对三维三温能量方程求解，使得计算量大大减少。
Based on the approximate analytic solution, the choked characteristics of flow in adiabatic capillary tubes are theoretically analyzed.
基于近似解，对绝热毛细管壅塞流动特性进行了理论分析。
By the parametric potential energy variational principle, the analytic solution of expansion problem of granular material pile is obtained.
利用参变量最小势能原理，求出了散体材料桩扩张问题的解析解。
It is very difficult to get analytic solution except some very specific cases for the model owing to nonlinear partial differential equation.
由于非饱和流动的数学模型归结为非线性的偏微分方程，除了一些很特殊的情况外，很难得到解析解。
This paper gives an analytic solution of non-circle opening based on linear viscoelastic theories and theory of function of a complex variable.
本文根据粘弹性体的理论与复变函数理论给出了非圆形巷道(洞室等)的粘弹性解析解。
Traditional knowledge about the rule of backwater length variation is reasonable, which is a special case of analytic solution to backwater length.
有关回水长度变化规律的传统认识有其合理性，它是回水长度解析理论的一种特殊情况。
In addition, an equation for calculation of maximum liquefaction depth is brought up according to analytic solution of saturated seabed under waves.
另外，论文还根据波浪作用下饱和海床响应的解析解提出了液化最大深度的计算公式。
In this paper, a formula of approximate analytic solution of subharmonic resonant overvoltage is established according to the theory of region analysis.
本文以区域分析理论为工具，提出分次谐波共振过电压的一个近似解析公式。
As an example, an approximate analytic solution of nonlinear vibration for a plate strip in lateral magnetic field is obtained by the multi-scale method.
作为具体问题，采用多尺度法求出了横向磁场中条形板非线性振动的近似解析解。
The recently proposed "analytic approximation solution" is proved to be a good approximation to the corresponding analytic solution under some conditions.
从精确解出发，推导出最近文献中提出的“解析近似解”，并指出该近似解的适用条件。
Analytic solution of temperature pattern of round heat sources is presented under the changing discharge channel radius with time and fixed input total power.
得到在随时间变化的通道半径和固定输入总功率表面热源条件下的温度场计算公式。
The result shows seven-freedom unit finite element method has high precision to analyse simple beam of rectangular section, it can replace complex analytic solution.
说明采用七自由度单元的有限元法进行矩形截面简支梁的弯翘分析，有很高的精度，可以代替繁琐的解析解。
The analytic solution for flowing field and the numerical solution for power law flow field of Newtonian and Bingham fluids flowing in eccentric annulus ale proposed.
提出了牛顿流体与宾汉流体在该偏心环空中流动的流场解析解及幂律流体流场的数值解。
The complex variable method analytic solution of stress is given for the plane elastic stress problem of surrounding rock of shallow circular tunnel under ground load.
采用复变函数解法，研究地面荷载作用下浅埋圆形隧道围岩的平面弹性应力问题。
Taking WEC of the river between Wushi Dam and Sanzhou Dam in the upstream as an example, two methods, the capacity definition method and analytic solution were compared.
以榕江上游乌石坝-三洲拦河坝段水环境容量为例，对容量定义法及解析解两种方法进行了对比研究。
A new analytic solution of the ballistic missiles reentry trajectory is presented by considering some more actual factors on the basis of the existing analytic solution.
在现有再入段解析方法的基础上，考虑更为贴近实际的条件因素，求得一组新的弹道导弹再入弹道解析解。
With the theory of elasticity, a model of induced stress field is established for primary fracture and the analytic solution is achieved by semi - retro-solution method.
应用弹性力学理论，建立了油气井中初次人工裂缝的诱导应力模型；并采用半逆解法得到初次人工裂缝诱导的应力场的解析解。
Then, the analytic solution of the geometrical nonlinear vibration system and the frequency-response properties of the actuator were analyzed by using multi-scale method.
应用多尺度法得到了超磁致伸缩换能器几何非线性振动系统响应的解析解和频响特性表达式。
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