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Concretely, firstly with Timoshenko beams, the fundamental formulae of solutions of dynamical equations, boundary conditions and initial conditions have been transformed by Laplace transformation. Secondly, in the Laplace regions , we gain the analytical solutions of impact forces at the impact contact points, shear and maximum inverse stress of beams. Then, by using Durbin numerical inverse method, we gain the numerical solutions of Timoshenko beams under various restriction conditions. Moreover, the graphs about impact forces at the impact contact points, shear and maximum inverse stress of beams can be obtained too.

把Timoshenko梁力学模型动力学方程的基本解形式、边界条件以及初始条件进行Laplace变换，在Laplace区域得到了冲击接触处的冲击力、整个梁的最大弯曲应力和剪力的解析解，然后利用Durbin数值反演的方法得到了各种约束条件下的Timoshenko梁模型时间-空间的数值解，得到了冲击接触处的冲击力、梁各处的最大弯曲应力和剪力的曲线图。

A third order ENO finite volume method for hyperbolic conservation laws on unstructured triangular mesh is introduced.In order to obtain the third order accuracy on spatial discretization,a weighted quadratic interpolation is constructed on every triangular mesh.Two point Gauss quadrature formula is also used on each edge of every triangular mesh and the third order TVD Runge-Kutta method is used for time discretization.The numerical order of convergence and the numerical result of a mesh 3 wind tunnel with one step are given.

摘 要 基于双曲型守恒律方程，对非结构三角形网格给出了一种ENO(Essentially Nonoscillatory Scheme)型有限体积格式，方法的主要思想是先对每一个三角形单元构造一个加权的二次插值多项式，而在计算交界面的流通量时采用了两点高斯积分公式以保证格式的整体精度，时间离散采用三阶TVD Runge-Kutta方法。

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。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。