查询词典 difference differential equation

This thesis is divided into six parts. The first chapter is preface, the current status of research in the inverse problems for parabolic partial differential equations is reported; the second chapter is "regularization methods for numerical differentiation and their applications ", in this chapter we investigate many regularization methods from a viewpoint of regularization theory and algorithm, some applications in the inverse problems for parabolic partial differential equations are given; the third chapter is "spectral regularization methods". Based on Fourier analysis, within the framework of regularization theory, we apply the spectral methods to some ill-posed problems. Many numerical experiments are done in order to show the validity of the methods; the fourth chapter is devoted to wavelet dual least squares method and a revised wavelet method; in the fifth chapter,we combine finite difference method with method of lines and apply it to the backward heat conduction problem in time; in the sixth chapter "identification problems for unknown source ", the essence and the degree of two problems related to source identification are pointed out, at the same time, some numerical methods are reported.

本文分为六个部分，第一章前言简要分析了国内外抛物型偏微分方程反问题的研究现状；第二章数值微分的正则化及其应用从正则化理论和算法的角度出发，考察了许多正则化方法，还给出了数值微分在抛物型偏微分方程反问题的一些应用；第三章谱正则化方法是在Fourier分析的基础上，在一般正则化理论的框架下，给出了这种方法在各种不适定问题中的应用，数值实验表明谱方法是有效的；第四章研究了小波对偶最小二乘方法和改进的小波方法；第五章主要研究了有限差分方法结合线方法在时间反向热传导问题中的应用；第六章是未知源识别问题，主要指出了两类未知源问题的不适定程度和不适定本质，同时报告了一些数值方法。

The finite difference method is applied to reduce the system of partial differential equations to ordinary differential equations.

采用有限差分方法，将由偏微分方程组描述的空间连续系统约化为由常微分方程组描述的空间离散高维动力系统。

The equations of the towed cable motion are based on Ablow and Schechter model and six degree-freedom ordinary differential equations are used in the analysis of the motion of a towed body. The partial differential equations are discretized by finite difference method and the transient values of towed body depth and cable tension are computed by Newton Iteration when the heave compensation system performs and the length of the cable varies.

拖缆动力学模型基于Ablow and Schechter模型，拖体采用水下运载体六自由度方程模拟，运用有限差分法离散偏微分方程组和牛顿迭代法计算变缆长情况下拖体深度与拖缆各点张力的动态取值。

Dry-type valves use air pressure and water pressure acting on both sides of the flap valve torque difference control valve on the valve closed and open, generally can be divided into differential-type dry-type alarm valve and sealed dry-type alarm 800X Differential By-Pass Balancing Valve valve two kinds of.

干式阀利用两侧气压和水压作用在阀瓣上的力矩差控制阀瓣的封闭和开启，一般可分为差动型干式报警阀和封闭型干式报警阀两种。

Based on the sliding response theory of the free-standing equipment, the differential equation of motion of the free-standing equipment under seismic excitations is presented. The equation is solved by Runge-Kutta algorithm, therefore the absolute acceleration, relative velocity and relative displacement of the equipment can be obtained. The sequential coulomb friction model is applied to the analysis.

以前人研究建立的浮放设备滑移反应分析理论为基础，给出了浮放设备在水平和竖向地震输入下滑移反应运动微分方程，选取连续型的库仑摩擦力模型，采用Runge-Kutta法求解浮放设备地震滑移反应运动微分方程，可以得到浮放设备在地震作用下的绝对加速度、相对速度和相对位移反应时程。

A differential equation for calculating squeeze-film air damping in slotted plates is developed by modifying the Reynolds equation.

推导出了一个适用于槽板结构压膜空气阻尼的微分方程。

The differential equation and algebraic equation are calculated separately so as to use proper methods based their own characteristics.

将微分方程与代数方程的解算问题分离，根据各自的特点选用适当的方法求解。

Put the discrete algebraic equations of initial derivative conditions and algebraic equation system of governing differential equation together to form a new algebraic system.

采用重心Lagrange插值近似未知函数，推导了未知函数各阶导数微分矩阵的显式表达式，建立了求解二阶常微分方程初值问题的重心Lagrange插值配点法。

The traditional method is to transfer the differential equation into the algebraic equation via orthogonal function. This paper adopts the advantage of Slant function including:(1) The characteristic that Slant operational matrix of integration changes fast can simplify the question.

传统的特性技巧是透过正交函将微分方程式转换为一个代方程式，本文采用其优点有：(1)用Slant 积分运算矩阵快速转换的特性可以简化问题。

It is generally difficult to get analytical solutions of the stochastic differential equation's water quality model. What is more, as to the issue like the initial boundary result of a convection-dispersion equation, it is even more difficult to change the random factors into the uncertainty.

NSFEM法是把Neumann展开式引入以解决矩阵求逆的效率问题，如果对每一次随机抽样，只需形成刚度矩阵，进行前代、回代以及矩阵乘和矩阵加减，而无需矩阵分解，则可大大减少工作量。

There had been a moment during the breakfast meeting, though, after the backslapping and the small talk and when all of us were seated, with Vice President Cheney eating his eggs Benedict impassively and Karl Rove at the far end of the table discreetly checking his BlackBerry, that I witnessed a different side of the man.

那次早餐会期间，在表示过关心和寒暄以后，我们所有人坐了下来，我注意观察了一下，副总统切尼面无表情地吃着班尼迪克蛋（Eggs benedict，源自美国，以英式松饼、火腿、水煮蛋以及荷兰酱组合而成），卡尔。罗夫在餐桌的远端谨慎地经常查看他的黑莓手机，我目睹了他所不为人知的一面。

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