数值分析

Whereas analytical method and the before-mentioned numerical method have some places to improve and the determination characteristics of satellite of middle-low orbit, this paper presents a new numerical project of determination of obvious characteristics on condition that range of determination is not very long and the precision of determiantion is the meter grade, and is realized by a software.

鉴于分析法定轨和上述通常采用的数值法定轨都有各自可改进之处，本文针对一般中低轨卫星定轨的特点，在弧段不太长和定轨精度为米级的情况下，给出一种具有明显特点的数值定轨方案，且以软件具体实现了这种方案，并经受了实测资料的考验。

The investigation for the interaction between planar moving shock wave and blast wave were carried out both numerically and experimentally.

通过数值模拟分析了不同条件下平面运动激波和爆炸波相互作用的特点，并通过实验进行了验证，数值模拟结果和实验结果吻合得很好。

In this dissertation, EISCAT radar observations and computer numerical simulation methods are involved to study the climatologic characteristics of polar ionosphere and their mechanisms, as well as the polar ionospheric responses to magnetospheric particle precipitation and convection electric field. Then, with the help of the numerical computation, the EISCAT data are employed to invert the energy spectra of auroral precipitating particles and their responses to magnetic storms and substorms.

本文联合利用EISCAT雷达数据和计算机数值模拟手段，以雷达探测数据为基础，数据分析和数值模拟、理论研究相结合，研究了极区电离层气候学特征与机制，磁层粒子沉降和对流电场对极区电离层的影响，并利用雷达数据反演极光沉降粒子能谱特征及其对磁暴和亚暴的响应。

The effects of cylindrical lens shape and the laser-fiber distance on relative coupling efficiency are also studied.

给出了一个计算980 nm泵浦激光二极管与柱形透镜光纤耦合角向容忍度的理论模型，并选择圆形的柱透镜光纤进行数值计算，得出了在水平和垂直方向上偏转加平移时的相对耦合效率及绕光纤轴向转动的相对耦合效率的数值计算结果并加以分析，同时也研究了光纤透镜的形状和激光二极管与光纤的间距对相对耦合效率的影响。

This paper measured the constitutive relation of soil in the condition of the low stain-rate by Split Hopkinson Press Bar technology. It offers the reference for study in high stain-rate in the future. And simulated the explosion between soil and concrete by finite element dynamic analysis software LS-DYNA3D. Finished the numerical simulation for power of exploding between soil and concrete in different position of detonator and different scale model. Set out the curves of displacement, velocity, acceleration and pressure of different position. Obtained the destructibility of concrete target in different explosion condition. It offers data reference for theory studying and engineering designing.

本文首先利用分离式Hopkinson压杆实验技术测定了土在低应变率下的本构关系，为以后进行较高应变率下的研究提供了参考；后面着重利用三维显式非线性有限元动力分析软件LS-DYNA3D对土壤混凝土介质中的爆炸进行了数值模拟，采用土壤混凝土分层介质模型，完成了不同装药位置、不同缩比模型的混凝土模型中爆炸威力的数值模拟，测定了不同情况下的压力曲线及典型位置的质点位移、速度、加速度和压力，得出了混凝土靶在各种不同爆炸条件下的破坏情况，为理论研究和工程设计提供了数据参考。

In order to analyze the influence of the center air pipe diameter change on the combustion effect, numerical modeling was applied to numerical calculation on the temperature field of such type of boiler,through which temperature field in five different schemes were obtained. In addition, the influence law of change of the diameter of the center air pipe on the temperature field was analyzed. The temperature of the nearly-back wall region takes on a firstly decreasing and then increasing change with the diametrical decrease of the central wind pipe.

为研究改变中心风管直径后的4层燃烧器对炉膛燃烧的影响，采用数值模拟的方法对该型锅炉炉内的温度场进行数值计算，得到5种不同方案下该型锅炉炉内的温度场分布，并分析了中心风管直径的改变对炉内温度场的影响规律，即后墙近壁区温度随着中心风管直径的减小呈现先降低后升高的趋势。

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中，首先从基本的分数阶常微分方程出发，对Lubich提出的一个关于分数阶导数的高阶近似，将其应用于分数阶微分方程，构造高阶数值差分格式来进行分数阶微分方程的数值求解，并在理论上给出这一算法的误差分析，证明了它的相容性，收敛性和稳定性。

In this dissertation, research work of near-field numerical simulation is briefly reviewed, some existing problems are analyzed, and the following problems in decoupling numerical simulation, which is a key research direction in present, are studied.

本文简要地回顾了近场波动数值模拟的研究工作，分析了存在的问题，并针对当前的一个主要发展方向—数值模拟的解耦技术，对下列问题进行了研究。

Based on these, a new numerical method for the Dirichlet problem is proposed in this thesis.

本学位论文，正是注意到了这些现象，提出了一种求解Dirichlet问题的新数值方法，克服了以往使用其它数值方法时常常遇到的困难和局限性，显示了分析数学中的问题借助概率理论来解决有着广阔的前景，在理论上和实际中都有着很好的意义。

Based on these, a new numerical method for the Dirichlet problem is proposed in this thesis. This method overcomes the difficulties and limitations resulting from others. It shows that solving problems in analysis by probability theory has a bright future both in theory and practice.

本学位论文，正是注意到了这些现象，提出了一种求解Dirichlet问题的新数值方法，克服了以往使用其它数值方法时常常遇到的困难和局限性，显示了分析数学中的问题借助概率理论来解决有着广阔的前景，在理论上和实际中都有着很好的意义。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。