数值方程

What's more, using edited computer program based on symbolic method, we can get the value of Riccati equation (which is the key to solving the optimal control law).

通过编制的计算机应用程序，运用符号法对Riccati方程(求解最优控制律的核心方程)进行了数值求解。

In Particular, the tangent stiffness matrix in the incremental relation becomes symmetric, ensuring the efficiency in the numerical analysis, whereas the integrated constitutive relation serves as a guide, ensuring the convergence on the physically feasible stress strain relation.

值得一提得是，增量本构方程中的切线劲度矩阵是对称的，使得在进行数值分析时十分有效。而全量本构方程作为确保实际可行的应力应变滞回圈收敛的向导。

In the numerical study, the governing equations of flow and heat transfer in 3 —D body—fitted curvilinear coordinate system being automaticly generated with TTM method were deduced by means of vector and tensor analysis. These equations were dliscreted with nonstaggered grids providing relative elimilating method for the pressure oscillation was domonstrated.

在数值分析中，借助于矢量理论和张量分析，导出了具有普遍意义的三维任意曲线坐标系下的流动传热控制方程，并利于TTM方法生成了计算域的贴体曲线坐标网格；在数值离散过程中，尝试了用非交错网格离散的方法并解决了压力场振荡的抑制问题；运用附面层理论，阐述了壁面函数法在三维任意曲线坐标系上的应用。

In the second chapter the theory of weighted residual technique is illustrated and the boundary integral function of the potential problem is deduced by it. Method of obtaining Greens function fundamental solution is presented. It also illustrates how to deal with inhomogeneous regions and the third boundary condition. At last the numerical solution of boundary integral function is presented.

第二章首先说明了加权余量法的原理，并由此推出了势问题的边界元积分方程，还介绍了无限域中格林函数的基本解的求法，以及多介质域和第三类边界条件的处理方法，最后说明了边界积分方程的数值解法。

After introducing the line tension contribution to the total Helfrich curvature energy, the axisymmetrical shape equation and the corresponding boundary conditions are obtained in the case of vesicle with one hole.

在得到关于开口泡的形状方程与相应的边界条件之后，本文进一步用数值方法求解了该微分方程。

The constructing process of the algorithms itself indicate that they are brevity and have definite geometric meaning, scientific iterative terminal criterions and no strict requirement to function. Finally, some digital experimentation is presented to indicate the algorithms application in solving the problem of maximum of function, transcendental equation,integer programming and so on. The results indicate that the algorithms have more global and more adaptability compared to traditional algorithms and have more calculating efficiency and more scientific iterative terminal criterions compared to some present popular artificial intelligence algorithms.

算法的构造过程本身表明了该算法简单明了、几何意义明确、迭代终止准则科学、对函数的要求较低；最后举了几个数值试验的例子以说明该类算法在求函数的最值，解超越方程以及整数规划等问题中的应用；数值试验的结果标明该算法比单纯由"微分"思想演化而来的传统算法有更好的全局性和对问题的更广泛的适应性，比现在流行的一些人工智能方法有更高的运算效率和更适当的迭代中止准则。

However, we can not get the film parameters directly because the ellipsometer equation is a transcendental equation. We can hardly get the analytical solution for film parameters from the measured ellipsometric parameters Ψ and Δ. Therefore, to find an algorithm to inverse the measured data Ψ and Δ becomes a primary but important problem.

但是通过椭圆偏振测量只能得到椭偏参数Ψ和Δ，由椭偏参数求解薄膜结构参数的椭偏方程是一个超越方程，很难得到精确的解析解，因此一般采用数值反演迭代不断逼近测量数据，将最优解作为测量结果。

On the base of other researcher, the *** from the basic equations of stable current field to derived the expressions of boundary problems under 3-D condition. Without considering the EM effect and using the generalized variation principle, we can get the corresponding variation equation. Thronging subdivide the 3-D model, interpolation, analysis, and general synthesis with the triangular prism element, we can carry out the simulation on frequency-domain IP\'s parameters under level and undulate topography.

在前人工作的基础上，在忽略电磁效应的情况下，从稳定电流场的基本方程出发，推导了三维区域满足的边值题目，用广义变分原理得到相应的变分题目，通过用三棱柱单元对大地模型进行剖分、插值、总体集成，最后解方程，得到每个节点上的复电位值，最后实现了水平和起伏地形等条件下的激电参数的数值模拟。2。

To solve the difficulties of digital integral that exist in global optimization of redundant manipulators, this paper discussed how to build up dynamic equation, the inner relation between constraints and unconstraint optimum control problems, then a digital method solving optimum control problems is deeply analyzed.

为了解决冗余度机器人全局法优化中数值求解的困难，本文讨论了动力学方程的建立、无约束和有约束最优控制问题之间的内在联系，重点分析了求解最优控制问题的数值方法。

It is proposed that the zero-point vibration term should be deleted in a thermal UEOS,and the parameters can not be directly taken as experimental data at a reference temperature,VR,BR,B′R and γGR,but their values at absolute zero temperature,V0,B0,B′0 and γG0.An approach is proposed to solve V0,B0,B′0 and γG0 from VR,BR,B′R and γGR.The approaches are applied to three typical universal EOSs,including the Baonza, mMNH and Vinet EOSs.

指出考虑热效应的通用状态方程中不应该包含零点振动项，方程参数不应该直接取为参考温度下的实验值VR、BR、B′R和γGR，而应该取为零温下的数值V0、B0、B′0和γG0；提出了一种从VR、BR、B′R和γGR求解V0、B0、B′0和γG0的方法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。