数值方法

In the last part of this paper, some numeral test functions were calculated by the software to test the efficiency of the algorithms included, then a reentry vehicle with cruciform flaps were taken as examples to testify the utility of Multi-Objective Optimization Algorithm Library.

在本文的最后，先用几个数值测试函数对方法库中几个产生式算法的性能进行了验证，然后用方法库对带控制舵再入飞行器进行了气动布局和外形优化。

And then, the theory of curve evolution, how to solve the PDEs model based on level set method and its calculation methods are expatiated.

其次详细介绍了曲线演化理论、偏微分方程模型的水平集方法求解以及数值计算方法。

In the last, three different algorithms (namely, the proposed algorithm, the traditional cutting plane method, and the discretization method) have been implemented for same problems.

最后，基于提出的修正算法，并与传统割平面方法、普通离散方法对同一问越作了初步的数值比较实验。

Then, based on temperature prediction program and field study of the temperature on early-age characteristics of PCCP, and early-age temperature impact on the PCCP early and long-term performance and finally provide temperature on early-age of PCCP control methods and measures, detailedness as follows: 1、According to early-age of PCCP characteristics of heat exchange, Determine the the optimal models of factors of PCCP early-age temperature impacted.

本文首先基于有限差分数值分析研究了水泥混凝土路面早龄期温度场的预估方法；然后基于程序和现场试验研究了水泥混凝土路面早龄期温度场特征、早龄期温度场对路面早期和长期性能的影响，最后研究提出了改善路面性能的早龄期温度控制方法和措施。

Numerical model tests show that the method proposed by this paper is as accurate as nine-point finite-difference when permeability tensor is in diagonal form, and it can simulate more complicated cases when permeability is in full-tensor form. Its application prospect is more extensive in fine detailed reservoir simulation.

模型计算表明，对于形式简单的对角渗透率张量，本文方法可以与九点差分格式相比，精度是可靠的，并且该方法还能模拟完全各向异性渗透率张量，对于精细油藏数值模拟，其应用范围将更为广泛。

The construction of the hamiltonian matrix, and the Lanczos exact diagonalization are also discussed.

并详细介绍了与该数值分析方法密切相关的Lanczos严格对角化方法，及构造巡游电子格点系统的Hamiltonian矩阵的技巧。

Finite difference method of one of the oldest numerical simulation methods, and it is used far-ranging recently.

有限差分方法是计算机数值模拟最早采用的方法之一，至今仍被广泛运用。

The finite difference method is one important numerical method for fluid dynamics.

其中有限差分方法是一种重要的数值计算方法。

By applying the explicit and implicit Euler methods to the neutral delay differential equation, two difference equations of the numerical solution are obtained.

把显式Euler方法和隐式Euler方法分别应用到这个中立型微分方程，得到了两个关于数值解的差分方程。

Spectral method is one of important numerical method for solving differential equations.

谱方法是微分方程数值求解的重要方法之一。

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。