The exact solutions are analytical physical solutions and can be served as accuracy checks for experimental, numerical and asymptotic methods.
这些精确解为实验，数值以及渐近解的检验提供了借鉴和参考。
For monolayer and two-layer spherical critical problem and for monolayer noncritical problem, the application by this approach gives the corresponding solutions and satisfactory numerical results.
运用这种方法对单层介质和二层介质的临界问题以及单层介质非临界问题进行了求解，而且得到了较满意的数值解。
The analytic solutions and numerical solutions of the equations of magnetic surface with fixed-boundary conditions are solved for the equilibrium plasma.
本文解出了具有固定边界的平衡等离子体磁面方程的解析解和数值解。
The paper introduce a weakly compressible flow model for small Machnumber. Both corresponding numerical solutions of the method and the applications are given.
介绍了小马赫数下弱可压缩流体流动的模型，对该模型的数值求解方法和应用情况也做了叙述。
On the basis of the asymptotic stability of generalized delay differential equations(GDDEs), the numerical solutions of one block methods for GDDEs were analysed.
在广义延迟系统渐近稳定的前提下，分析了用块方法求解广义延迟系统数值解的稳定性。
Finally, the numerical analysis for the solutions with different bias against the risk is presented.
最后，对不同风险偏好下的解进行了数值比较分析。
Besides having the significance in theory, they can also be the standard solutions for checking various numerical solutions and methods.
这些解除在理论上有其重要意义外，还可以用来作为检验各种数值解的标准解之用。
The principles and performance of the ice force oscillator model are presented in the paper, and its numerical solutions for a single degree of freedom system are demonstrated.
本文叙述冰力振子模型的建立原则及其特性，并给出一单自由度系统的数值解。
Numerical solutions for retouchment length and velocity-distributions -were obtained in the recirculating zone of the combustion chambers.
得到了燃烧室内回流区再附长度及速度分布的数值解。
Secondly, a technique of numerical order verification was applied to verify that the asymptotic solutions were uniformly valid for small parameter.
其次，一种数值阶验证技术证实求得的二阶渐近解对小参数都是一致有效的。
The heat transfer mathematic model for solar marsh gas pit was set up based on the test results. It is shown that the good agreement between the numerical solutions and experiment data.
同时建立该沼气池的传热数字模型，获得了模型的数值解，实验结果和计算结果相互校验，最后整理得出了池温的分布规律。
Besides the significance in theory, they can also be the standard solutions for checking various numerical solutions and methods.
这些解除在理论上有其重要意义外，还可以用来作为检验各种数值解法的标准解之用。
Such numerical solution is iterated for all the waves with different frequencies, and all the numerical solutions are transformed into the light fields in the time domain by inverse Fourier transform.
然后把这种数值解方法分别运用到所有频率的单色波即可就出其对应的光场，而且对所有的这些数值解作逆付里叶变换就可以将其转换为时间领域的光场。
The numerical solutions of VSL equation sets in one-temperature and two-temperature cases are obtained for flows in the stagnation region of a hypervelocity blunt body.
采用单、双温度模型两种粘性激波层方程组对弹头驻点区非平衡流场作了数值模拟。
The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equations.
两种模型正合微分方程的解析解与数值解表示出十分的吻合。
The numerical results agree with those of available literatures and show that the method is robust and stable for getting the discontinuous solutions of the shallow water wave equation.
计算结果与已有文献结果基本一致，证明该方法有效、稳定，能够模拟浅水长波方程中的间断解问题。
This dissertation was to study the mathematical theories and methods for structural dynamical model updating. It gave the solutions and the numerical methods of a special structure model updating.
本文主要研究结构动力模型修正中的数学理论与方法，研究了一类特殊结构模型修正问题，并为线性结构有限元动力模型修正提供了有效的数值方法。
The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exa...
两种模型正合微分方程的解析解与数值解表示出十分的吻合。
Traditional solutions for the characteristic impedance of asymmetric rectangular coaxial strip-line (RCSL) were obtained mainly with the aid of numerical methods.
传统的非对称矩型同轴线特性阻抗求解往往借助复杂的数值方法。
Theoretically, the entire information for the shock can be obtained by sorting to the numerical solutions to the set of ODEs easily.
理论上讲，借助数值求解该常微分方程组便可得到有关激波的主要信息，结果将为行星际激波求解提供便捷的途径。
For more complex problems, it is difficult to present the analytical solutions and numerical simulation is a kind of effective method.
对于较复杂的现实问题，很难用解析的方法求解，而数值模拟是一种有效的求解方法。
The close agreements of the numerical solution for several cases with other solutions indicate that our solution is satisfactory.
在几种情况下与其它解进行了比较，结果是令人满意的。
The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equation…
两种模型正合微分方程的解析解与数值解表示出十分的吻合。
We prove that the iterative solutions converge to the exact solutions for any initial values. The algorithms proposed require less storage capacity than the existing numerical one...
分析表明：在任意有限初始条件下，迭代解收敛于精确解，提出的算法需要较小的计算量和存储空间。
This method and the numerical solutions show that the method is also suitable for pure mathematical optimization problems with 0-1 discrete variables.
该方法对于纯数学的0 - 1离散变量优化的求解也适用，方法与数值都表明了这一点。
The process parameters can be optimized and the errors can be evaluated for numerical solutions more precisely.
由此可加深理解渗碳过程的物理本质，优化渗碳工艺技术参数，并可作为评定数值解误差的最好依据。
Adaptive meshes in the numerical simulation for shell forming can achieve solutions of required precision using as little calculation as possible and increase the precision of the solutions.
板壳成形数值模拟过程中用自适应网格不仅可以实现以尽可能少的计算量获得指定精度要求的解，更重要的是可以提高解的精度。
The numerical examples show that this method is effective for obtaining the solutions of dynamic response.
实例表明，该方法是求解动力响应问题的一种非常有效的方法。
The numerical examples show that this method is effective for obtaining the solutions of dynamic response.
实例表明，该方法是求解动力响应问题的一种非常有效的方法。
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