数值方法

Since the 19th century, classical celestial mechanics system and the formation of planets and the moon Sports theory has become a complete theory of .19 century to the 20th century, 50 years is the period of modern celestial mechanics, improved analytical methods, additional qualitative methods and numerical methods .50 years after the study of celestial mechanics celestial object from the solar system be extended to man-made objects Movement Theory, as well as a few star systems, broadening the field of study.

此后到19世纪末，经典天体力学体系形成，大行星和月球运动理论已成为完善的理论。19世纪末到20世纪50年代是近代天体力学时期，改进了分析方法，新增加了定性方法和数值方法。50年代以后，天体力学的研究对象从太阳系天体扩展到人造天体运动理论以及为数不多的恒星系统，拓宽了研究领域。

Therefore, the primary purpose of the present study is to construct the projection methods in higher order accuracy. Furthermore, the proposed projection methods will be applied to nonstaggered grids, curvilinear coordinates, and moving mesh cases.

因此，本文从提高数值方法计算精度入手，构造了高阶时间精度的投影方法，并将投影方法推广到非交错网格和一般坐标系及动网格中。

The meshless local Petrov-Galerkin method is a new numerical technique presented in recent years, for it doesn't need any element or mesh for the energy integral or the purpose of interpolation, and it's termed as a truly meshless method.

无网格局部Petrov-Galerkin方法是近几年发展起来的一种相对较新的数值方法，它不需要借助任何的单元或网格来进行积分或插值，是一种真正的无网格方法。

In order to avoid the singularity in the integration, the integrand was expressed to be sum of complex exponential terms by using discrete complex image method. With generalized pencil of function method introduced, the number, location and intensity of images were obtained without extracting the quasi-static and surface wave terms in the integrand, which makes DCIM more efficient for multi-layered media.

为了避免积分中的奇异性，利用离散复镜像法将积分核用复镜像的指数求和式表示，引入广义函数束方法，可以在不提取积分核中表面波项的条件下，采用数值方法提取准静态项，给出复镜像点的数目、位置和强度，使得该方法在多层介质情况下对格林函数的计算更为有效。

In the second part,we have mainly discussed the error es-timates of the numerical methods for solving ill-posed problem,including the error estimate of finite-dimensional regulariza-tion method in Chapter 5,and the error estimate of regulariza-tion-spline method for solving Fredholm integral equation ofthe first kind.

在第二部分，我们主要讨论了不适定问题数值方法的误差估计，包括有限维正则化方法求解不适定问题的误差估计以及用样条正则化方法求解第一类Fredholm积分方程的误差估计，两者均是目前还未有的结果。

In the case of simply supported ends, the Galerkin method is used to simplify the integro-partial-differential equation into an integro -differential equation. The equation is further simplified into a set of ordinary differential equations by introducing an additional variable. Finally, the numerical methods in modern nonlinear dynamics such as phase plane trajectory, power spectrum and Lyapunov exponents are adopted to investigate the dynamical behavior of the beam.

对于两端简支的情形，采用Galerkin方法简化为常微分－积分方程；然后通过引进附加变量的方法进一步简化为常微分方程；最后利用相平面图、功率谱和Lyapunov指数等非线性动力学中的数值方法识别梁的动力学行为。

At present, trust region method and line search method are two mainly types numerical algorithms for nonlinear programming.

目前，信赖域方法已经和传统的线搜索方法并列为非线性规划的两类主要数值方法。

The analysis of the optical signal transmission characteristics and the physical parameters provides the theoretical foundation for optimizing the design and improving the performance of AWG; and the optimizing design numerical value calculation method solves the complex problem of the optimizing design of the AWG, it can also provide a way for AWG computer aided design system; the AWG optical signal processing analysis provide a way for optical signal Fourier transform, serial and parallel transmission, circle shift, matrix transform and differential processing; the optical signal processing characteristics of AWG develop AWG to use for new field, and the optical signal processing will play an important role on all-optical networks in the future; by the definition of the wavelength transform matrix of the AWG, the signal output positions that come from these input signals of the different wavelength or the same wavelength but the different input ports and carrying different signals can be accurately determined, and the wavelength transmission matrix plays an important role for analyzing the routing of the complex optical network, or designing the network nodes such as the optical path add/drop multiplexer and optical cross connect device; the wavelength transmission matrix also provides a method for monitoring and managing the wavelength transmission of the optical network nodes; e analysis of the AWG' OXC node structure and wavelength routing provides a way for realizing the OXC, especially for multi-path/multi-wavelength OXC and the intelligence node of the optical networks; by the studying of the control plain characteristics, router, traffic engineering, program and the improved arithmetic of the wavelength routing, the method for realizing the GMPLS' OXC optical transport network is provided, and it play an important role for the study of the automatic switched optical network; the time-frequency analysis can provide more information about the dispersion and energy changes of .the pulsed light transmission in the singlemode fiber, it also provides more useful parameters for analyzing the dispersive accumulating and dispersive compensating.

AWG光信号传输特性与相关参数的分析，为进一步优化设计AWG及提高其性能提供了理论依据，而优化设计计算数值方法解决了AWG优化设计计算的复杂问题，为进一步建立AWG的计算机设计系统提供了基础；AWG光信号处理的特性分析，提出了AWG应用的新领域，为光信号的傅立叶变换、串并传输、循环移位、矩阵变换、微分处理等提供了一条途径；波长传输矩阵变换关系的建立，不仅得到了确定多路AWG每路信号从输入端口到输出端口的准确输出位置的方法，而且在分析应用AWG实现复杂的光通信网络路由的连接、特别在设计分插复用器和交叉连接器等网络节点时有重要的作用，能有效而准确地确定波长的路由关系，为实现节点波长传输路由的监控和管理提供有效手段；基于AWG的OXC结构和波长路由的确定为实现OXC技术、特别是多路多波长的OXC和光网络的智能节点技术提供了有效的方法；控制平面的特征、路由器、流量工程、程序及改进的波长路由算法的研究实现了基于GMPLS的OXC光传送网络的控制平面，为建立自动交换光网路提供了一定的基础；时频分析可以更直观和更清晰地描述脉冲信号在单模光纤中传输色散和能量的变化，为色散积累和色散补偿提供有效的分析参数。

By employing a new pattern of combination, in which the analytic method is the basis and the numeric method is the reinforcer, the composite Fourier series method is proposed in the thin plate bending problem.

提出薄板弯曲问题的复合傅里叶级数方法。它以解析方法为融合基体，数值方法为融合增强相，是一种新的融合模式。

The numerical results show that the vibration effect of the pressure plate inside the printhead plays an important role in the inversion stage of the printing process.

结果发现，研究中的数值方法能够顺利预测喷墨头内外流场，数值模拟之新月形气液界面线，在喷墨头作动的吸入阶段中，预测值与实际值相似。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。