差分方程

Lastly, we study a model of the heat flow cryptosystem base on a linear pseudoparabolic equation. The C-N difference scheme arithmetic of the encryption and decryption problems is designed. Then the numerical simulation is done through computer programming. So by analysing the simulation data we deduce many regularly conclusions on the influence of the key functions to the encryption and decryption operations, which establish the theoretical base for the application of this cryptosystem.

最后，文章研究了一类基于线性伪抛物型方程的热流密码体制模型，设计了加、解密问题的C—N差分算法并通过计算机编程进行了数值模拟，得出了一些不同密钥函数对加、解密作业影响的规律性结论，为该密码体制的现实应用奠定了理论基础。

In order to obtain the variation law of temperature during casting solidification to improve casting quality,a finite element method combining with a finite difference method was used to discretize time and space variables in the governing equations of astable heat-conduction in the process of casting solidification so as to obtain the algebraic equations for casting and mold temperature.

为了掌握铸件凝固过程中温度场的变化规律以提高铸件质量，采用有限元和有限差分相结合的方法离散铸件凝固过程非稳态热传导方程的空间和时间变量，得到了关于金属铸件和铸型温度的代数方程。

And the energy balance equation is applied to describe the temperature field axial orientated.

对流道的径向瞬态温度场分布进行差分求解，对流道轴向的温度分布运用能量平衡方程建立数学模型，并采用松弛迭代求解；最后，考虑流动和冷却过程的温度场分布，对流道径向和轴向温度场的计算结果进行了耦合分析，解决了长期以来只能依靠经验计算热流道温度场的局限。

Those equations are dispersed in space by iso-parameter elementmethod and in time by using backward difference. A numerical simulator is established byFortran, the ideas of high part make the of structure program clear, maintain easy, calculationeffective.

在此基础上利用Fortran语言编制了有限元方法的油藏模拟器，采用等参元对渗流方程在空间上离散，采用向后差分在时间上离散，线性方程组的求解采用变带宽高斯消去法，该方法充分利用刚度矩阵呈条带状和其对称性的特点，大大减少了所需存储空间。

This paper presents a fast algorithm based on the measured equation of invariance.Conformal meshes are made along the surface of two-dimensional scatterer.Renumbering of nodes changed the original sparse matrix into band one,and the consumption of computer memory and CPU time decrease from O(N2) to O.Via this new algorithm,electrically large problem can now be rapidly solved.

提要 本文基于不变性测试方程法提出一种快速算法，在二维散射体表面建立共形差分网格后，通过对节点的重新排序，将原问题中的稀疏矩阵变换为带状稀疏阵，从而使占用的计算机内存和计算时间均由O(N2)下降为O，可以解决原来无法计算的问题。

And that method is different from the adding base point method and impact method from importing derivatives of higher order.

他与增加基点数目的方法和引入高阶导数的紧致方法不同，是微分方程差分近似高精度化的一种新方法。

The thesis is organized as follows:In Chapter 1,a new partial differential equation model for Spontaneous Potential log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.

具体安排如下：第一章首先建立复杂地层中自然电位测井的偏微分方程数学模型，证明了该边值问题弱解的存在唯一性，在此基础上研究了自然电位测井电阻率识别问题：然后发展了用于求解椭圆交界面问题的间断捕捉有限差分方法，利用该方法定量分析了目的层电阻率、地层厚度、井径、侵入带和水淹层等因素对自然电位测井响应的影响，取得了满意的结果。

Preserved-amplitude migration ; One-way wave equation ; Fourier finite difference ; Migration operator ; Boundary conditions ; Imaging conditions

保幅偏移；单程波方程；傅里叶有限差分；偏移算子；边界条件；成像条件

As a result of the interpretation of the discrete random walk model,the stability and convergence of the numerical method in a bounded domain are discussed.

接下来提出求解有界区域内的Lévy-Feller对流-扩散微分方程的显式差分格式，并且利用前面随机游走模型中的结论证明了显式格式的稳定性和收敛性。

For raising the precision of solving infiltration in unsaturated soil, by reviewing advantage, and disadvages of existing methods, based on the transformation of Richards equation, a finite calculus of differences by advancing front self-adaptive grid for solving infiltration in unsaturated soil is built.

为提高非饱和土壤渗透求解的精度，综合考察现存方法的优缺点，通过理论研究，基于Richards方程变换，建立了非饱和土壤渗透求解的向前探索自适应网格有限差分法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。