差分方程

It is shown that in Jameson's algorithm is not an orthogonal stream-lines coordinate system, but a local stream-lines coordinate system instead. Nevetheless, because of the finite-difference discretization in Jameson's scheme is not carried out along the direction of s and n, but along the Cartesian coordinates, the analysis on all terms of the full potential equation in Cartesian coordinates reveals that his scheme does take a back-ward difference along the streamwise exactly at all points in the supersonic flow region.

表明其所采用的坐标系不是真正的正交流线坐标系，而是局部流线坐标系；同时由于Jameson方法并不对s，n进行差分离散，而是在原笛卡尔坐标系下作差分离散，对笛卡尔坐标系下的全位势方程中的各项的分析表明，Jameson方法恰好能做到在超音速点沿真正的流线方向作后差分。

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

A new scheme for approximating the solution of 2D Maxwell's equations-the high order symplectic scheme is proposed to overcome the shortcoming of the conventional finite difference time domain. The scheme is obtained by discretizing the Maxwell's equations in time domain based on symplectic scheme with high order, and then evaluating the equation in spatial domain with second or fourth order finite difference approximation.

为克服标准时域有限差分方法的缺陷，引入一种新的数值计算方法－高阶辛算法求解Maxwell方程，即在时间上用高阶辛差分格式离散，空间分别采用二阶及四阶精度的差分格式离散。

In the two-dimensional simulation, the fully implicit difference scheme is used for the continuity equations to ensure numerical stability; Jacobian iteration is used to solve the difference equations, and only nonzero elements in the coefficient matrixes of these equations are dealt with, which reduce the requirement for memory and shorten the calculation time.

在两维模拟计算中，对连续性方程采用全隐式差分方案以保证数值稳定性；运用雅可比迭代法求解差分方程组，并且在求解过程中，只对差分方程组系数矩阵中的非零元素进行处理，因此减少了对内存的需求量，而且缩短了计算时间。

To price the continuously sampled arithmetic average Asian option, an implicit upwind difference scheme is constructed based on the final boundary value problem of partial differential equation, which is satifiable to the option pricing problem. Then the unique existence and unconditional stability of the difference solution are demonstrated and the error estimate is given under the discrete L2 norm.

研究连续取样的算术平均亚式期权定价问题的差分方法，根据问题所满足的偏微分方程终边值问题，构造出一种隐式的迎风差分格式，论证了差分解的惟一存在性和绝对稳定性，并给出差分解在离散L2范数下的误差估计。

This thesis carries on research to a class of nonlinear Schrodinger Equation with wave operator of initial value periodic problem.

本文针对一维带波动算子的Schrodinger方程周期初值问题进行数值研究，对上述方程首先构造了守恒的半离散格式，然后将p次Hermite插值方法与有限差分方法相结合构造了差分正交样条配置格式，并证明这两个格式均为稳定和收敛的格式。

In this paper, we present a class of equation model for image denoising and edge enhancement. The model is based on robust statistics error norm and variational theory.

本文基于稳健统计误差模函数及变分原理构造了一类用于图像去噪、增强边缘的方程模型，对相关参数进行了分析，设计了该方程有限差分数值求解的并行算法，并对分块模型及实现过程进行改进，提高了并行效率，在此基础上完成了并行数值实验，并对结果就误差模选取、并行效率等方面进行了分析。

In this paper difference equation of motion fr om one point to another point on the earth is derived from the geodesic equation on the earth and spherical trigonometry formulas. Some difference track formul as of a maneuvering object are also given.

以大地椭球三角形模型为基础，利用地球表面二点间最短路径的大地线方程和球面三角形的有关公式，建立了由地球表面一点运动到另一点的差分运动方程，同时也给出了在进行航向机动时的差分运动轨迹。

In this paper differ ce equation of motion fr om one point to another point on the earth is derived from the geodesic equation on the earth and spherical trigonometry formulas. Some difference track formul as of a maneuvering object are also given.

以大地 椭球三角形模型为基础，利用地球表面二点间最短路径的大地线方程和球面三角形的有关公式，建立了由地球表面一点运动到另一点的差分运动方程，同时也给出了在进行航向机动时的差分运动轨迹。

With the consideration of various factors affecting on the screening effect,a screening model for drilling fluid shale shaker had been established.

利用流体力学的基本原理，对钻井筛筛面上钻井液的流动特点进行了研究；在综合考虑有关参数对钻井筛筛分影响的基础上，建立了钻井筛的筛分模型，给出影响钻井筛处理量有关因素之间的定量关系；运用平均值法对筛分方程的求解进行了探讨；应用有限差分方法建立了筛分方程的仿真模型，并编写了钻井筛处理量的计算机仿真程序。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。