差分方程

In order to investigate and develop numerical calculation method for Schr odinger equation, we apply the finite difference method to eigenvalue problems in quantum mechanics.

为研究和发展薛定谔方程的数值计算方法，本文将有限差分法应用到量子力学求解薛定谔方程本征值问题。

Based on the limitation and tightness of computational time, it is concluded that the neighborhood of the equation solution is solvable under the condition of open solvable set.

研究了用差分法求解自治的发展方程时稳定性和收敛性这两个基本概念之间的联系，利用计算时间的有限性和紧致性，在可解集为开集的条件下，得出方程解的邻近也可解的结论。

By use of the time split method, a conservation difference formula is established to find the solution to the shallow water equation based on the finite volume control method from integral equations.

作者中文名：李光炽；王船海；周晶晏摘要：采用二分步法，从积分型方程出发，在有限控制体上建立守恒型差分格式，对二维浅水波方程进行求解。

It is shown that such a model can be used to design a nonlinear controller by techniques of norm H(subscript ∞) with the goal of maintaining relative equibalance water level along the open-channel reach.

以节制闸紧急启闭造成的水位波动和渠道物理建模的不确定性为抑制目标，采用泰勒级数和基于泛函估计有限差分法对Saint-Venant方程进行逼近形成了有限维状态方程，在H范数意义下对模型进行求解。

The nonlinear hyperbolic conservation laws of the transient flow of the media in gas pipeline are hard to he solved, so, the control conservation laws are constituted of mass, momentum arid energy conservation laws, TVD/Godunov hydrid algorithm is used to simulate the transient flow in gas pipeline, and the traditional splitting approach processing nonlinear convection in momentum equation is dismissed ,the convection tern; is directly processed, in the way, the stablization of the algorithm and emulating accuracy of the transient flow are greatly improved.

针对管道中介质瞬变流动的非线性偏微分方程组难以解析求解的问题，由质量、动量、能量三个偏微分方程构成的控制方程组，应用TVD/Godunov混合算法数值模拟天然气管道中气体的瞬变流动，摒弃了传统的差分方法时动量方程非线性时流项的线性化处理，而直接处理非线性对流项，从而大大提高了算法的稳定性和管道瞬变流动的仿真精度。

The article first theoretically analyzes the principle that microcavity reduces threshold 、changes resonant modes of output light and enhances unidirection of the random laser.Then study the structure parameters of different microcavity by transfer matrix.Based on the theory of Maxwell equations and the rate equations, analyze the principle that microcavity reduces the threshold by FDTD method: Changing the confined position,reducing relaxation time and increasing reversing particles, also simultaneously study the influences of the threshold and output light modes by different microcavities and random intensity of random medium.

首先从理论上分析了利用微腔降低随机激光器阈值、改变出射光振荡模式、提高出射光准直性的原理，然后利用传输矩阵法模拟研究了不同的微腔应具有的结构参数，最后以麦克斯韦方程和速率方程理论为基础，利用时域有限差分法分析了利用微腔降低阈值的原理：改变局域化位置、缩短弛豫时间及增大粒子数反转，同时也模拟研究了微腔、随机介质的随机强度对阈值及出射光波模式的影响。

This paper presents a numerical model for solving problems of water and contaminant transportion and transformation in variably saturated porous media.

本文采用有限差分法离散水流方程和污染物浓度方程。

Based on the theoretical model coupling Maxwells equation with the rate equation of 4 level inverted population, the numerical simulation is made via the FDTD method and MATLAB programs. The simulation results show that 1. With the increase of the pumping rate, both the localization of the electric field and the spectrum mode numbers will change; 2. The lasing threshold decreases by increasing the size or concentration of the scatters; 3. The lasing threshold also decreases by increasing the size of samples or strengthening the sample randomness.

在理论和实验研究的基础上，利用麦克斯韦方程与四能级反转粒子数的速率方程相耦合的理论模型，采用时域有限差分方法和MATLAB程序对随机激光泵浦阈值特性进行了数值模拟与计算，模拟结果显示：随着泵浦速率的增大，出现了阈值前后电场强度局域态及频谱模式数的改变；随着散射体粒径的增大，浓度的增大，阈值呈现下降的趋势；随着样品长度的增大，随机强度的增强，阈值也呈现下降的趋势。

A numerical solution of the isothermal EHL problem for finite line contacts has been pressnted which is convergence in moderate load and material parameters.

二。用差分格式离散二维Reynolds方程，通过间接求解的方法，推出了中等载荷和材料参数下收敛的等温有限长线接触弹流数值计算方法，有效地克服了等温有限长线接触Reynolds方程的强各向异性所产生的数值计算易发散问题。

It was presented that a dynamic retrieving differential equation mode of two-variable hydrologic time series considering one main cycle.

3提出一种考虑一个主周期的水文二元时间序列动力反演微分方程模式，并应用双向差分法和最小二乘法推导微分方程参数，给出求解公式。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐