差分方程

An extended hyperbolic mild-slope equation, which can take such terms as wind input, bottom friction and nonlinearity of wave into account, here has been deduced into a parabolic one in the form of a series of governing equations described with complex amplitude. It became a complete wave model when integrated with corresponding physical and imaginary boundaries, and can be solved through the improved Crank-Nicholson or the well known Alternating Direction Implicit difference method, both of which can accelerate the convergent speed , expand limitation of the mathematical method and improve the quality of the solution.

本文基于综合考虑底摩阻、风能输入及非线性影响的推广双曲型缓坡方程，将其进行转换，产生一个演变方程，其复振幅控制方程为抛物线性，并采用ADI差分格式、改进的Crank-Nicholson格式及相应的物理和虚拟边界条件进行求解，以提高数值模拟的适用性、数值计算的稳定性、收敛速度及精度。

But the finite difference methods require that the compu-tational domain is regular,and usually people construct the finire differencescheme for one dimension and then extend it to two or three dimensions in adimension by dimension fashion.

但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。

If the neighborhood of equation solution is solvable and meets the point- by-point Lipschitz condition, stable boundary could be obtained as the convergence of the difference method is realized, and thus the stability is ensured.

方程解的邻近如果可解并具备逐点Lipschitz条件，则差分法收敛必有稳定界存在，从而差分格式收敛性保证其稳定性，因此可以放弃线性这一重要条件。

The initial-boundary value problem of dispersive equation is a kind of mathematical model, in this paper, it has been followed the ways of other scholars and used a new method and got a new difference scheme. It was a three layers ten-point implicit difference schemes.

色散方程的初边值问题是在孤立波这样的物理现象中抽象出来的一类数学模型，在前人构造的众多差分格式的基础上，使用新的构造方法，给出了该问题的三层十，点隐式差分格式。

Based on the analysis of the traditional absolute difference positioning th eory, the relative pseudorange difference positioning technique was researched and the equation of state which solves r elative position was given.

在对传统的绝对差分定位原理进行分析的基础上，研究了相对伪距差分定位技术，得到了求解相对位置的状态方程。

By using the Eulerian-Lagrangian combined method, the convection-diffusion equation is spitted into the diffusion terms and convection terms. For convection terms, the implicit method of characteristics using time-line interpolation with high accuracy is adopted. While for the diffusion terms the conventional finite difference method is used.

采用欧拉—拉格朗日混合解法，将对流—扩散方程中的扩散项和对流项分裂求解，应用高精度时间序列插值的特征差分隐格式求解对流项，扩散项采用传统的有限差分法。

Equations are differenced by control volume algorithm , convection term is differenced by up wind difference algorithm , diffusion term and continuity equation are differenced by central difference algorithm .

采用控制容积法对控制方程组进行离散，对流项采用迎风差分格式，扩散项、连续方程采用中心差分格式。

For example, a regenerative reheating furnace fluid flow and heat transfer is researched, which has simplified the flow and heat transfer of hot air stove according to its real operating conditions.The fluid flow and heat transfer of a hot air stove are numerically simulated by using finite volume method or finite difference method,which bases on the heat transfer equation,flow equation of the gas and heat balance equation.

根据热风炉的实际运行状况对蓄热式热风炉内的流动换热过程进行了合理的简化，并基于热传导方程、气体流动方程和气体的热平衡方程，建立了蓄热体的非稳态传热模型，在对模型利用有限差分法和有限容积法得到离散方程的基础上，采用C 语言编制了模拟计算程序。

The wave equation of electric in the waveguide can be translated into a coupled difference equation of second order by centered differency approximation.

通过中心差分法可将电场满足的波动方程化为一组耦合二阶差分公式形式。

The finite difference time-domain method is stable and easy to be used, but due to the fact that it approximates the space derivatives in Maxwells curlequations by central difference, FDTD usually requires more than 20 grids perwavelength to achieve acceptable accuracy. As a contrast, pseudospectraltime-domain method approximates the space derivatives by pseudospectralmethod, which guarantees the accuracy, theoretically requiting only 2 grids perwavelength.

传统的电磁场数值算法——时域有限差分法稳定而易于实现，但由于FDTD采用中心差分近似Maxwell旋度方程的微分，每个波长上需要取的网格数通常较多，而时域伪谱法采用伪谱法求微分，理论上每个波长只需要取两个网格便可以达到较高的精度。

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。

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