差分方程

Therefore scientists have been engaged in research on approximate solutions of the partial differential equations,e.g.,the difference methods,the methods of characteristic curve and MWR method etc.,i.e., by using approx...

因此不少研究分布参数系统的科学工作者对这方程式近似方法进行了大量的研究，如差分法，特性曲线法和MWR法等；或者把分布参数系统近似成集中参数系统，或者把高价方程简化为低阶方程等。

The control volume integration was applied to deduce the discrete expressions of the convection-diffusion equations. The staggered grid and SIMPLE algorithm were introduced to deal with coupling between pressure and velocity, and then the numerical computation expressions of such variables as fluid flow velocity and pressure were deduced. Using the backward difference method and incremental theory to discretize the governing equations for fields of chemical reaction, material structure and chemorheology, the numerical computation expressions of variables such as the monomer conversion, average molecular weight and fluid viscosity were constructed.

应用控制容积积分法导出了对流—扩散方程的离散表达式，引入交错网格技术与SIMPLE算法，实现了耦合的压力场与速度场的分离式求解，推导得到了流体的流动速度、压力等物理量的数值计算式；采用向后差分方法和增量方法，实现了化学反应场、材料结构场、化学流变场控制方程的离散，获得了反应转化率、聚合物平均相对分子质量、流体黏度等物理量的数值计算式。

Tridiagonal block matrix elemination and sweep algorithm is successfully applied to solve the large matrix involved; central difference method is supplemented to Houbolt method to form a time integration method with estimation and correction, to solve the time integration of second order implicit non-linear equation; simplification of system equation by decoupling between the physical coordinates x and y further improves the calculation accuracy and speed.

其中：成功地引入块三对角矩阵追赶法求解上述问题构成的大型矩阵；提出中心差分法+Houbolt法的预估计—校正时间积分法，以解决二阶隐式非线性方程的时间积分问题；系统方程在物理坐标x和y上的"解耦"简化，使计算速度和计算精度得以进一步的提高。

In this research, the plane 2D mathematical model under Cartesian coordinate system and the

首先建立了直角坐标系正交网格下的平面二维数学模型及复杂边界适体坐标条件下的三维紊流数学模型，对方程的离散差分格式、控制方程的求解、初始边界条件、动边界处理等问题进行了分析研究，并编制相应的计算程序。

On detailed study of the central difference finite volume method proposed by Jameson, discrete formulae of 3-D Euler equations and N-S equations are presented.

详细研究了Jameson的中心差分有限体积法，推导了Euler方程和N-S方程的空间和时间离散公式。

The model is applied to numerically analyze the wave field and the coastwise current formed by the breaking of oblique incident wave in the Leadbetter Beach, Santa Barbara, California, USA. In the analysis the Crank-Nicolson scheme is adopted to solve the parabolic mild slope equation and the ADI finite difference scheme is applied to solve the model of wave induced coastwise current.

运用该近岸流方程，对美国Santa Barbara Leadbetter海岸波浪斜向入射所产生的波浪场及波浪破碎所形成的沿岸流进了数值模拟，其中抛物型缓坡模型采用Crank-Nicolson格式进行数值离散，近岸流方程采用ADI差分格式离散。

VOF equation use Lax-Wendroffgeshi scheme with precision of two steps. Pressure of host field is turned into initial-boundary value problem of variable coefficient parabolic equation on regular border. We utilize implicit difference method to solve it.

VOF方程的离散求解使用Lax-Wendroffgeshi格式，这种格式具有二阶精度；主场压力的求解转化为固定边界上变系数抛物型方程的初边值问题，采用隐式差分格式。

The PSE in the curve coordinate systems are solved by the numerical techniques developed efficiently in this paper. A normal transform is introduced, and there are enough much grids in the region between the critical layer and the wall, where the variation of the disturbance is the quickest. The finite-difference of governing equations with fourth-order accuracy in the normal direction is utilized in full regions including points close the wall, and is very important for accurately discreting equations.

对于曲线坐标系下的抛物化稳定性方程，文中发展了求解的高效数值方法：引进法向变换，使得在临界层与壁面之间的扰动量变化最快的区域有更多的法向网格点；导出包含边界邻域在内的完全四阶精度的法向有限差分格式，这对方程精确离散至关重要；采用全局法和局部法相结合的方法及其新的迭代公式，大大加速收敛并得到更精确的特征值。

First, the mathematical model of the HT oxide crystal growth is set, and then the dimensionless equations are given out. Finally, the boundary conditions are determined and the equations are solved by FDM. The simulation program is given by the above method.

首先建立了高温氧化物晶体生长的数学模型，然后给出了无量纲方程，最后确定了边界条件，使用有限差分方法求解了方程，并在此基础上编制了仿真程序。

Firstly, based on the wave equation, determining reasonably its initial boundary condition, the paper establishes a computer diagnostic model of oil pumping mechanical well, the damping factor in the model has been reasonably determined, the implicit difference solutionis conducted to the model by changing of step width expression difference solves, and the half analytical solution is explored to the model - fine integral method; and realizes the transformation from dot indicator diagram to indicator diagram of any section.

首先从抽油机井计算机诊断技术的理论基础入手，考虑多级抽油杆连续性，建立了粘滞阻尼波动方程，合理确定模型中的阻尼系数，采用无条件稳定的隐式差分法及半解析方法求解方程，获得抽油杆柱任意断面和抽油泵处的示功图。

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