数值

Finally numerical examples with three shape functions are analyzed in detail. The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also one or higher orders derivative.

最后，通过多个数值算例的计算比较了三种形函数的计算结果，结果显示本文提供的MGMLS方法关于函数值和各阶导数值都具有很高的精度。

The discrete velocity ordinate method in the kinetic theory of gases is developed and applied to discretize the correspo

借助非定常时间分裂法和无波动无自由参数的NND耗散格式，建立直接求解微观分子速度分布函数的有限差分数值格式；研究并发展可用于离散速度坐标点选取和离散速度空间宏观取矩的高斯─埃尔米特无穷积分方法、等均间隔的牛顿─柯斯复合积分法、以勒让德多项式的根为积分结点的高斯─勒让德数值积分法，并应用于不同马赫数绕流模拟；通过对不同流域一维激波管问题、二维圆柱绕流问题和三维球体绕流的计算研究，并将计算结果与其他途径得到的研究结果诸如DSMC模拟值、N-S解及有关实验数据进行比较分析，创建了一套能有效模拟稀薄流到连续流不同流域气体流动问题简化的统一数值算法研究框架

In this paper,we give the error expressions of piecewise linear Lagrange polynomial interpolation and piecewise cubic polynomial interpolation using the Taylor expansions.

中文摘要：本文利用Taylor展开得到三角形上线性Lagrange插值和三次Lagrange插值的导数余项公式，对这些余项公式进行分析，给出了两类能以四阶精度逼近被插函数在对称点的导数值的格式，一种是在均匀剖分时其分片线性插值的相邻单元的导数值的后处理格式，一种是在六片强正规剖分时的三次插值在对称点上的导数值的后处理格式，使得在已知原函数在各节点的值后，通过一个简单的线性计算就可得到原函数在对称点的导数的一个超逼近值，将以往提出的平均导数的二阶精度提高到四阶。

The author also writes a great amount of numeric computational sub-programs and programs too, almost include all respects of structural numeric computation using Daubechies wavelet. These programs not only test and verify the correlation results in this thesis, but also lay a strong foundation for expanding the application space of Daubechies wavelet in structural numeric computation.

本文还编制了大量的数值计算子程序和计算例程，几乎囊括了Daubechies小波有关结构工程数值计算的所有方面，这些程序的编制，不仅验证了本文的相关结论，同时，也为后续进一步拓展Daubechies小波在结构工程数值计算领域的应用空间打下坚实的基础。

The numerical examples show that the modifying generalized moving least squares approximation has high accuracy not only for function value but also first or higher orders derivatives.

数值计算显示本文提供的方法关于函数值和各阶导数值都具有很高的精度。

And the author integrated the ship maneuvering, numeric analysis, the solution method for inverse problems and the control theory, and made the decision that the regularization method is adopted to obtain the coefficients of ship maneuvering, and that immune genetic algorithm is used as the numerical algorithm of the regularization method.

通过分析，综合船舶操纵性，数值分析，反问题的数值解法和控制理论等相关知识，决定采用正则化方法反演船舶操纵运动相互干扰系数，用结合免疫遗传算法的正则化方法作为数值解法来建立船舶操纵运动灰箱模型。

Owing to the drawbacks of analytical shimming, this paper puts forward the concept of passive numerical shimming for searching a method of compensating Bz'easily to a high level and with a low cost. Based on the magnetic field caused by a magnetic moment, the distribution of moments in a superconducting NMR imaging megnet can be determined through some pseudoinversion algorithm directly from Bz'. The moments are used to compensate Bz'.

无源数值匀场的出发点直接是不均匀磁场的磁场偏差B〓本身；无源数值匀场的基础为磁性材料的磁矩所产生的磁场；由已知B〓，通过某种逆运算，确定磁性材料的磁矩在主磁体中的分布，实施此分布，以磁性材料的磁矩所产生的磁场直接对B〓进行补偿——这便是本文提出的无源数值匀场的概念。

This paper brief introduce numerical method of algebraic equation,points out their shortcoming of missing multiple root and put forward one new kind of method--multiple derivation numerical method.

本文对通常代数方程的数值计算方法特点进行了简介并给以分析，指出了这些解法无法得出重根数的缺陷，提出了一种新的解决方法———多次求导数值计算法，使得数值计算法更加清晰、明了，且可得出重根数。

The effect of the elastic-plastic matrix of friction soil with nonrelevant flow rule on the numerical convergence of finite element method is analyzed in this paper; and the effect of elastic modular, poisson ratio and earth pressure coefficient on numerical results are studied in this paper. At the same time, the hybrid element with a mixture of displacement and stress variables and the conventional element with solely displacement variable are compared when used in geomaterials.

在ABAQUS有限元分析软件的基础上，本文研究了服从非关联流动法则摩擦性土体的弹塑性矩阵对有限元数值算法的影响，并研究了弹性模量、泊松比以及地基土压、力系数对数值计算结果的影响，同时探讨了数值分析过程中常规位移元与杂交元在岩土工程中的应用。

Based on the numerical simulation algorithm in this paper, numerical results for temperature field are given and analyzed.

基于我们构造的三维温度场数值模拟算法，给出了变压器运行过程中温度场在空间与时间分布的数值结果，并对所得到的数值结果进行了分析。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。