数值微分

The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算，将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程，再由反射图方程和图像梯度信息构造目标方程，进而用Newton迭代算法求出该方程的数值解，得到表面三维形状。

It is also shown for the first time that DQEM could be regarded as the combinations of the sub-domain method with the special mixed collocation method.

微分求积法和微分求积单元法是在近年里发展起来，并正在进一步发展的一种数值计算方法，本文对这两种方法的原理和它们在结构力学中的应用进行了较深入系统地研究。

The coefficients in trial function can be gained by the point collocation method, then the solution of the boundary value problems is obtained. Non - uniform beams and irregular plates on Winkler foundation and plates on elastic half space foundation can be numerical calculated by the introduced method.

为对土与结构物的相互作用进行研究，在采用适当的土体模型的基础上，必需求解地基与基础的共同作用方程，而该共同作用方程一般是偏微分方程或微分积分方程，除一些简单的模型外，其解析解较难获得，因此只能采用数值方法求其结果，加权残仇法是一种L作鼠少、简便易行的数仇方法{2，但其解的精度'。

In mathematics, Chinese scholars have achieved important results in fields such as number theory, theorem-proving by computer, differential geometry, topology, complex analysis, probability and mathematical statistics, PDE, functional analysis, numerical analysis and control theory and so on.

在数学方面，据我所知，中国数学家在诸如数论、定理机器证明、微分几何、拓扑学、复分析、概率论与数理统计、偏微分方程、泛函分析、数值分析和控制论等领域里也都取得了具有国际水平的成果。

In this project, we develop the numerical model of the differential quadrature element analysis of beam problems considering the effects of shear deformations. The results demonstrate this method.

在这个计画中我们开发剪变形梁问题的数值积分表示微分元素分析的数值模式，并做数值计算，证明此种方法的优越性。

Based on modern optimization theory and optimal control theory, this dissertation studies some questions as follows:1. The optimization model of parameter identification of three-dimensional geologic history numerical simulation, algorithm and its applicationGeologic history numerical simulation is a basic content of basin numerical simulation, and the porosity is the major parameter in the evolution and development process of oil-bearing basin. According to the sedimentation and burial mechanism, the physical and chemical principles of oil geology, the mudstone porositys non-linear parabolic partial differential equation has been established.

本文应用现代最优化及最优控制理论，对如下一些问题进行了研究： 1、三维地史数值模拟的参数辨识优化模型、算法及应用地史模拟是盆地数值模拟的一个基础性的研究内容，地层孔隙度是含油气盆地地史演化发育过程中的重要参数，根据地层沉积埋藏机理和石油地质的物理化学原理，通过引入数学物理方程概念，建立了泥岩三维孔隙度场方程，根据问题的特点，给出了方程的定解条件，对方程的动边界也给出了处理方法，并且证明了解的存在性与惟一性，在此基础上建立了以当今实测数据为拟合准则的三维地史数值模拟的参数辨识优化模型，这是一个含有二阶偏微分方程约束的泛函极值问题。

Aim To study the numerical solving process for the large sparse matrix linear equations. Methods To realize the above aim, program developing language C++, cross list data storage structure, the special method of pivoting and elimination of pivot element were adopted.

大型稀疏矩阵线性化方程组的数值求解问题，广泛存在于工程实践尤其是计算机仿真领域，如水力管网计算 [1] 、电力系统的大型导纳矩阵计算、高阶偏微分方程的数值求解[2 ] 以及铸件充型过程与凝固过程的数值模拟等。

In the third chapter, the contractilities and asymptotical stabilities of neutral delay integro-differential equations are concerned. The extended Runge-Kutta methods, with the compound quadrature formula and the Pouzet quadrature formula, are numerically stable under suitable conditions. The numerical experiments prove this result.

第三章，研究了中立型延迟积分微分方程，其理论解的收缩性和渐近稳定性，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，并获得了数值方法的稳定性条件，随后的数值试验结果进一步证明了方法是数值稳定的。

Using a one--dimensional differential thermocline model, we simulated the temperature and thermocline of Yellow and Bohai Sea.

本论文建立了黄渤海环流的三维斜压模式，进行了黄渤海三维环流的数值模拟研究，另外，用一个温跃层一维微分模式对黄渤海的温度及跃层现象进行了数值模拟，最后，建立了一个黄渤海温度及环流的数值模式。

We take the nonlinear Klein-Gordonequation in an infinite strap and in a cylinder as examples to illustrate how to deal withnonlinear problems by using Jacobi pseudospectral methods.

Jacobi谱方法和拟谱方法数值分析理论的研究极大地丰富了现有谱方法的理论基础，同时将发展泛函分析、数值逼近论和偏微分方程数值解的相关理论。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。