差分方程

In order to get the numerical solution, the paper devises a three hierarchic implicit scheme which eliminates the strict restriction of explicit scheme, thus, it can be used in more areas. By using the energy estimation method, the convergence and stability of the difference scheme are proved and the scheme is second order convergence for time and space.

对求解方程构造了一个三层隐式差分格式，消除了显格式的稳定性对计算步长的严格限制，使之适用范围更广，并用能量估计的方法严格证明了差分格式的收敛性与稳定性，该格式对于时间和空间均具有二阶收敛性。

Space fractional differential equation ; finite difference approximation ; stability ; convergence

空间分数阶微分方程；显式有限差分格式；隐式有限差分格式；稳定性分析；收敛性分析

For convection dominated diffusion equations with constant coefficients, the implicit scheme is consistent,unconditionally stable and its L~2 error estimation is derived.

对常系数的对流占优扩散方程而言，基于一边有限差分和中心差分的隐格式是相容的并且无条件稳定，对应L~2误差估计被推导。

Based on Crank-Nicoson's technique, and a new approach for the numerical simulation of the model is raised. The truncation error of the one step difference method reaches O (△t^2+△x^2) and of quite good stability condition.

基于Coriolis加速度和Lagrangian应力公式，利用Newton第二定律导出轴向加速度运动弦线横向振动的动力学模型；通过线性变换将方程化为一阶无量纲的非线性微分方程组；并利用Crank-Nicoson的中点离散技巧，给出运动方程的单步二阶差分方法；算法把对运动方程和本构方程分别离散，使之可以用于不同本构的运动弦线的数值仿真。

First,we construct the finite difference scheme of the equation,the existence and the uniqueness of the solution for the scheme are proved.

首先，构建原方程的有限差分格式，并验证了差分格式解的存在唯一性。

A 2-D coupled numerical model, which is the combination Boussinesq equations solved by finite difference method with Laplace equation solved by boundary element method, is established.

Boussinesq方程与Laplace方程耦合计算模型：1 建立了外域用有限差分法求解Boussinesq方程、内域用边界元法求解Laplace方程的二维耦合计算模型。

With the knowledge of linear algebra, general formula for arbitrary order Taylor finite difference has been derived. In this paper, the analysis of spectral property and computational error of arbitrary order TFD is presented in detail. Then it is applied into the numerical solution of Maxwell's equations. Stability condition and numerical dispersion relation are derived.

本文借助于采样定理，详细分析了不同阶Taylor中心差分格式的谱特性以及计算误差，并将任意阶Taylor中心差分格式用于数值求解麦克斯韦方程中，严格导出了稳定性条件和数值色散关系的表达式，引入了新的误差定义来衡量算法的好坏。

It adopts the variable step length scheme to evaluate at the connection point, and adopts the implicit difference scheme to evaluate in the same rod.

3运用在均质处采用隐式差分格式、节点处采用变步长的有限差分的混合方法求解抽油杆柱的波动方程。

The constitutive equation between current density vector and electric field strength vector is tranformed into s-domain by the principle of Laplace transform,and the inverse Laplace transform is adopted for the explicit equations between them in time-domain. Finally through exponential time stepping,the FDTD iteration equations are obtained,which can be easily solved in discrete-time-domain.

该方法是将电流密度矢量与电场强度矢量之间的本构方程基于拉普拉斯变换原理转到复频域，然后再逆变换到时域得到它们之间显式的方程，最后再结合指数差分，得到离散时域的显式的FDTD迭代方程，解决了本构方程中电流密度矢量的分量相互耦合而不易直接离散的困难。

But the finite difference methods require that computational domain is regular, and usually people construct the difference scheme for one dimension and then extend it to two or three dimensions in a dimension by dimension fashion.

有限差分方法要求计算区域比较规则，而且人们往往是对一维方程构造差分格式，再用分裂方法将其推广到多维。

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