数值方法

Some numerical examples are given to show that the numerical method presented is an approximation method with high efficiency and convergence.

数值计算表明本文数值方法是一种高效和收敛的近似方法。

In this work, we mainly study the numerical analysis of bifurcation theory, especiallythe numerical computation of Takens-Bogdanov point in delay differential equations.

本文中，我们主要考虑分支理论的数值方法，具体而言，时滞微分方程中Takens-Bogdanov点的数值计算方法。

To RPC, the fluidity was usually a key index, because it directly reflected the work-ability. The effect factors were complex, however, the quantity relation between the RPC fluidity and its effect factors could not be expressed with a uniform numeric formula. There was no effective method for this problem at present. In accordance, a numeric method which used for controlling the RPC fluidity was advanced. The neural network model based on genetic algorithm was introduced for a aptitude method consequently.

流动度是RPC配制的一个关键指标，它直接反映了其工作性的优劣，但其影响因素复杂，难以用统一的数值关系直接描述RPC流动度与其影响因素的量化关系，目前还没有合适的计算方法，为此，提出控制RPC流动度的数值方法，即引入遗传神经网络对RPC的流动度进行预测控制。

Based on these, a new numerical method for the Dirichlet problem is proposed in this thesis.

本学位论文，正是注意到了这些现象，提出了一种求解Dirichlet问题的新数值方法，克服了以往使用其它数值方法时常常遇到的困难和局限性，显示了分析数学中的问题借助概率理论来解决有着广阔的前景，在理论上和实际中都有着很好的意义。

Based on these, a new numerical method for the Dirichlet problem is proposed in this thesis. This method overcomes the difficulties and limitations resulting from others. It shows that solving problems in analysis by probability theory has a bright future both in theory and practice.

本学位论文，正是注意到了这些现象，提出了一种求解Dirichlet问题的新数值方法，克服了以往使用其它数值方法时常常遇到的困难和局限性，显示了分析数学中的问题借助概率理论来解决有着广阔的前景，在理论上和实际中都有着很好的意义。

It is usually that the solution for the Dirichlet problem can not be obtained actually. With the development of computers, people pay more and more attention to the numerical solution. Many ideas and methods have appeared. Among them the finite element method has become most popular. But the finite element method has some weaknesses and limitations too. First, it is not fit to higher-dimensional problems.

绝大多数Dirichlet问题的解析解往往难以得到，随着计算机技术的发展，Dirichlet问题的数值解法越来越受到人们的重视，新的思想和方法不断涌现，其中有限元法已经发展成为目前求解Dirichlet问题的最主要的数值方法，但是有限元法解决该问题时，存在着一些弱点和局限。

It is usually that the solution for the Dirichlet problem can not be obtained actually. With the development of computers, people pay more and more attention to the numerical solution. Many ideas and methods have appeared. Among them the finite element method has become most popular. But the finite element method has some weaknesses and limitations too.

绝大多数Dirichlet问题的解析解往往难以得到，随着计算机技术的发展，Dirichlet问题的数值解法越来越受到人们的重视，新的思想和方法不断涌现，其中有限元法已经发展成为目前求解Dirichlet问题的最主要的数值方法，但是有限元法解决该问题时，存在着一些弱点和局限。

According to the properties of Wiener increments and the independent relation between the Wiener increments and the numerical solutions, the difference equation obtained by applying the numerical method to the general linear test equation is studied carefully in mean square sense and the conditions under which the numerical method is MS-stable and GMS-stable are determined.

依据维纳增量的性质以及维纳增量和数值解间的独立关系在均方意义下详细分析了数值方法应用到线性试验方程上得到的差分方程，并进一步确定了半隐式Milstein方法MS-稳定和GMS-稳定的条件。

In this dissertation, based on the discussed history of numerical method of structure-born sound radiation, the boundary element integral equation is deduced, and then the numerical method of sound radiation, the theory of radiation modal and the sound radiation sensitivity analysis is discussed in details.

本文在分析了结构声辐射数值方法的历史及其现状的基础上，详细推导了结构声辐射的边界积分方程，对声辐射的数值计算方法、声辐射的模态理论以及声辐射的灵敏度分析作了深入详细的探讨。

The theoretical development of internal flow of turbomachinery is then summarized in terms of separation theory, vortex dynamics and flow pattern.

然后分别从分离流动理论、涡动力学和叶轮机械流型三个层次介绍叶轮机械内部流动理论的发展；从平面叶栅、环形叶栅、动态试验和试验技术等方面回顾叶轮机械试验研究进展；从控制方程、数值方法、网格生成等方面综述叶轮机械数值计算研究方法、研究内容及成果等，并概括改善叶轮机械气动性能的方法和现状。最后对叶轮机械内部流动研究进行展望。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。