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Under the one-dimensional situation, it introduces mainly the Newton-Cotes formula, the Gaussian quadrature formula, the numerical integration rule of sharp oscillatory function, the numerical integration rule by the methods of sampling and so on.

在一维情形下，主要介绍了Newton-Cotes公式，Gauss型求积法则，急速振荡函数的数值积分法则，抽样法求数值积分的法则等。

With the knowledge of linear algebra, general formula for arbitrary order Taylor finite difference has been derived. In this paper, the analysis of spectral property and computational error of arbitrary order TFD is presented in detail. Then it is applied into the numerical solution of Maxwell's equations. Stability condition and numerical dispersion relation are derived.

本文借助于采样定理，详细分析了不同阶Taylor中心差分格式的谱特性以及计算误差，并将任意阶Taylor中心差分格式用于数值求解麦克斯韦方程中，严格导出了稳定性条件和数值色散关系的表达式，引入了新的误差定义来衡量算法的好坏。

This paper analyzes the characteristics of graphical solution method, analytical equation method and numerical method, then discusses finite element method and forward step method of the numerical method.

分析了图解法、解析法和数解法等水力解析方法各自的特点，并着重比较了有限元法和Hathoot前进法等数解法的优点和局限性。

Based on the study of a discrete chaotic system of numerical solution and graphical simulation, while for discrete time-delay chaotic system a numerical simulation procedure.

详细说明：摘要：基于研究了离散混沌系统的数值解法和图形仿真，同时针对离散时滞混沌系统给出了数值仿真的程序。

This paper analyze and study the influence of the superimposition in depth based on the previous achievements and combined with the theoretical qualitative analysis and project instances. The main contents as follow:Chapter 1: Indicate the significance and objective of this paper, review the previous achievements of the transient process and superimposition, and then present the study purpose of this paper.Chapter 2: combined with the physic knowledge of the fluctuation and the superimposition, Indicate the physical essences and the influence of the superimposition phenomena that exist in the diversion pipe system, and take one hydraulic turbine owning only one diversion tunnel and two hydraulic turbines sharing one tailrace conduit for instance to study out the numerical calculation superimpose operations.Chapter 3: From the calculation theory of the parameter of the guaranty calculation of regulation of the hydro-turbine, qualitative analyze the influence of the superimposition on them and the superpose time, combined with some project instances, get the numerical value of the influence of the superimposition and the superpose time.Chapter 4: Based on the previous achievements of the calculation and theoretical analysis of the surge-chamber ground swell, analyze the influence of the superimposition on it and the superpose time.

本文在前人研究成果的基础上，结合理论定性分析及工程实例，对波动叠加带来的影响进行深入分析研究，其主要内容如下：第1章，指出本文研究的意义和目的，回顾前人对水电站过渡过程及波动叠加方面的有关研究成果，在此基础上提出本文的研究内容；第2章，结合物理学中有关振动与波动叠加方面的有关知识，阐述水电站引水发电系统中存在的波动现象的实质及其影响，并以两机一洞和一机一洞具有上游调压室或下游调压室的水电站拟定其数值计算叠加工况；第3章，从机组调保参数的理论出发，定性的分析波动叠加对机组调保参数的不利影响及叠加时间，结合几个工程实例，得到波动叠加带来的影响大小及叠加时间；第4章，在前人对调压室涌浪进行计算和理论分析的基础上，分析波动叠加对调压室涌浪的影响及其叠加时间。

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。

To assess our numerical method, several cavitating flows over the hydrofoil were computed and the numerical results were compared with experimental results.

通过将半球圆柱的计算结果与实验数据和前人的计算结果进行对比，验证了所发展的数值方法的可靠性。

The powerful function of a new computer language MATLAB, produced by the America Mathworks company, is the mathematical software system for the calculation in science engineering. It can efficiently solve problems in science and engineering such as numerical linear hypercomplex system, digital approximation, optimization, numerical quadrature etc. It also has characters of beautiful interface and convenience for users.

MATLAB是Mathworks公司推出的适用於科学和工程计算的数学软件系统，可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题，且具有可视化图形处理、使用方便、开放式多功能於一体的新一代计算机语言。

To provide theory foundation for inverted deduction work, numerical simulation for propagating in highway-surface with exceptional block and inanition and crack has been performed. The numerical simulation results show that the BEM is an effective method for the elastic-waves propagating in highway-surface concrete medium.

利用边界元法能够很好的描述弹性波在砼介质中传播的特性，正演模拟异常石块、脱空和裂缝对波的传播的影响，为进一步的反演工作提供理论依据。

The authors make basic research for the numerical calculation of cooling waters flow in the engines, on the bases of research results obtained with numerical method of incompressible fluid.

本文在作者已完成的不可压缩流体三维流动数值模拟研究的基础上，对发动机冷却水三维流动的数值模拟方法进行了基础性研究。

The dynamic variation in content of cndogenous abscisic acid,indoleacetic acid,gibberellinsand isopentenyladenodines of normal juvenilefruit and dropped fruit was measured with enzyme linked immunosorbent assayin the course of physiological fruit drop of 'Shuizhang Longan.

应用酶联免疫法测定了水涨龙眼生理落果期间正常幼果和脱落幼果中内源激素ABA、IAA、GAs及iPAs含量的变化。

Zillions of code examples on the web.

网上数量巨大的代码例程。