数值方法

The main works in this paper are as follows:(1). In this thesis, a new method, continuous linearization model, is constructed for the non-linear dynamic systems. The precision Duhamel integration solution for the linearization equation is also given from the theory of linear differential equation. The calculating results show that the new method can improve the calculation precision greatly. In fact, the truncation error is not limited by this method, it can arrive the precision according to the requirement.

本文的主要工作有以下几个方面：(1)由于非线性项的存在，使得多数情况下难以得到非线性动力方程的解析解表达式，目前常使用数值积分方法来求解非线性动力学方程的解，但常规计算方法的计算精度不很理想，本文提出了含Taylor展开项中高阶余项的非线性动力方程的线性化数值计算方法，构造了瞬态线性化方程，给出了Duhamel积分的表达式。

Here, the theory and the deducing process of the SEM based on the Legendre polynomial is given. The SEM can get a global diagonal mass matrix, which leads to a very simple explicit time difference scheme and high efficiency. Numerical simulation in the transversely isotropic medium are shown and the results approved that the SEM is a effective method for seismic wave modeling.

文中阐述了基于Legendre多项式的谱元法的理论和推导过程，该方法可以形成全局对角质量矩阵，在时间域使用显式的差分算法，提高运算效率，最后通过横向各向同性介质的数值计算，模拟结果表明该方法是一种有效的数值模拟方法。

The SEM can get a global diagonal mass matrix, which leads to a very simple explicit time difference scheme and high efficiency. Numerical simulation in the transversely isotropic medium are shown and the results approved that the SEM is a effective method for seismic wave modeling.

文中阐述了基于Legendre多项式的谱元法的理论和推导过程，该方法可以形成全局对角质量矩阵，在时间域使用显式的差分算法，提高运算效率，最后通过横向各向同性介质的数值计算，模拟结果表明该方法是一种有效的数值模拟方法。

Firstly, Wavelet-Galerkin algorithm for solving the first kind of singular integral equation with the Hilbert kernel is proposed, we use the characteristic of periodic wavelet on L~2([0,1]) and Hilbert kernel to solve and make stiff matrix lower dimensions and become sparser through thresholding,thus the cost of computation is reduced. Because of the singularity of Hilbert kernel we use Tikhonov regularization method to solve the system of stiff equation. At last the convergence and numerical result of approximate solution are given. Secondly, an approach of regularization based on Fourier is presented for sideways heat equation; we give the theory proof and error estimate.

首先，提出了含Hilbert核的第一类奇异积分方程的小波伽辽金(Wavelet-Galerkin)数值算法，该算法中利用了L~2([0，1])上的周期小波和Hilbert核的特点进行处理，使得刚性矩阵维数降低并且通过阈值使得它更加稀疏，减少了计算量；由于Hilbert核的奇异性，通过Tikhonov正则化方法求解所得到的刚性方程组，给出了收敛性和数值结果；其次，对标准的一维逆热传导方程给出了一种基于Fourier正则化方法，给出了理论证明及其误差估计，解决了文献中算法与理论误差估计的不相匹配的现象，该正则化方法不仅保留了测量数据的部分高频成份，且与文献中的算法具有同样的计算量和误差估计。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

It is proved that numerical simulation is a efficiency method for researching the microbus s temperature field by compare the numerical simulation result with the experiment result.

通过计算和试验结果的对比分析，说明数值计算方法是研究微型面包车温度场的一种有效方法，采用数值计算方法可以比较精确的模拟微型面包车温度场的分布情况。

On the basis of the results of survey and study about researches of pulse well test at home and abroad, the method of total pressure history match and numeric solution is selected as an advanced research, the goal is to investigate a method of pulse well test in theory and analysis under the conditions of no knowledging about the changing tendency of formation pressure and having outer boundary.

根据对国内外关于脉冲试井研究情况的调研结果，本文选择全压力史拟合方法和数值求解方法作为一个探索性研究课题，将有限元法应用于压力的数值求解过程，目的是探索一种在地层压力变化趋势不清楚和有外边界的条件下的脉冲试井理论和分析方法，从而为油田提供结果更准确的、信息更丰富的开发调整依据资料。

In the second chapter, generalizing the contractilities and asymptotical stabilities for multi-delay integro-differential equations. Under proper stepsize, we obtain the discretization schemes of Runge-Kutta methods with the compound quadrature formula and the Pouzet quadrature formula, and besides, derive the global and asymptotical stabilities. Moreover, the numerical experiments show that the presented methods are highly effective.

第二章，考虑了多延迟情形下的积分微分方程，推广理论解的收缩性与渐近稳定性结果，在适当的步长下，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，获得离散的计算格式，并且证明了方法是数值稳定的，此外，数值试验表明此计算方法在实际应用中是非常有效的。

Based on the science idea of coupling, this paper studied systematically the theory, mathematical model and technology of rock mass hydraulics in coal mining above aquifer, the numerical simulation method, the resemble simulation theory and method. A series of reciprocity law on the stress and displacement of upper and down floor of coal layer, coal pole, fault and the law of water pressure variety was analyzed thoroughly and particularly. Based on the relation of hydraulics character of multi-aquifer, the inspecting and predicting theory model, method and system of water outburst was founded. By used in the colliery, The results were ratified by colliery missionary. In situ test for the hydraulics character of the floor on hydrology observation hole was done.

本文基于固流耦合作用的学术思想，通过理论研究、相似模拟实验、数值分析及现场实际应用，系统研究了带压开采的块裂介质岩体水力学数学模型，数值模拟方法，相似模拟理论与方法，深入细致地分析了带压开采中项底板、煤柱、断层的应力位移分布、含水层水位变化等一系列相互作用规律，并建立了基于多含水层水力联系的底板突水监测预报理论模型及其监测预报方法与系统，并将研究成果应用于现场实际，得到了现场工作人员的一致认可。

At first, on the basis of the combination research methods of analytical theory, numerical simulation and experiment, the mathematical and physical model of certain-length rolling process have been established. Then according to the established model, the menstruation of rolling average friction coefficient is proposed; and then the certain-length rolling process and key parameters are determined.

采用理论研究、数值模拟和实验研究相结合的研究方法，建立定长轧制物理模型和数学模型；基于所建模型，提出了一种测定轧制平均摩擦系数的方法；确定了定长轧制工艺方法和关键参数；分析了影响制件轧制长度的因素；对关键参数进行了数值模拟。

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。