数值方程

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。

It is not only introduced the two measures taken to solve the biharmonic equations , but the topical grids of H-type、C-type 、 and O-type are generated with this equation.

文中不仅对数值求解双调和方程的两种不同方法作了介绍，还利用该方程生成了典型的H型、C型、O型网格。

In the numerical simulation, the Blasius equation of boundary layer based on the Chebyshev interpolation points was solved by using of the Runge-Kutta method with variable step.

在数值模拟中，采用变步长的Runge-Kutta方法，求解基于Chebyshev插值点的边界层Blasius方程，然后对边界条件进行坐标变换，使Chebyshev谱方法适用于边界层稳定性方程的求解。

In the numerical simulation, the Blasius equation of boundary layer based on the Chebyshev interpolation points was solved by using of the Runge utta method with variable step. On the basis of the coordinate transformation of the boundary condition, the Chebyshev spectral method was applied to solve the hydrodynamic stability equation of boundary layer.

在数值模拟中，采用变步长的Runge Kutta方法，求解基于Chebyshev插值点的边界层Blasius方程，然后对边界条件进行坐标变换，使Chebyshev谱方法适用于边界层稳定性方程的求解。

In particular, we expound Einstein field equation and its numerical approach when a neutron star is rotating and collapsing, and discuss the moments of Boltzmann equation and its observation when a neutron star is rotating only.

特别，我们论述了有转动有塌缩情况下Einstein方程及其可能的数值解法，以及有转动时Boltzmann方程的矩形式及与观测的联系。

First, we discuss the noncharacteristic Cauchy problem for 1-D heat equation.

首先，对一维的热传导方程的非特征Cauchy问题，我们利用边界积分方法将问题的求解转化成解积分方程组的问题，再对积分方程组进行离散化来数值求解，最后的数值结果表明我们的算法是有效的。

In the numerical calculations,the unknown density of dislocation is approximated with the product of fundamental function and Chebyshev polynomials.The calculations show the present method yields rapidly converging and high accurate numerical results.

在数值求解这组奇异积分方程中未知位错分布密度近似为基本密度函数与Chebyshev多项式之积，计算表明，本文方法的数值结果不但收效快而且精度高。

Numerical computation part includes detailed study on theoretical numerical models and preliminary study on the 1999 Chi-Chi, Taiwan, earthquake.

数值计算部分的工作主要包括两部分：针对构造的理论数值模型详细研究在各种因素影响下的半空间中断层上的自发破裂行为，以及利用本文建立的方程初步研究1999年台湾集集地震的动力学破裂过程。

The different methods for establishing the equations of vehicle-bridge system are summarized and assessed. The vehicle-bridge coupling relationship, including the geometrical compatibility condition and the static equilibrium condition at the interface of wheel/rail, is established. The forces on the vehicles, which coming from bridge deflection and track irregularity, and those on the bridge, which coming from vehicle deflection, are given. Then, the governing equations of vehicle-bridge system are setup.

提出了车桥系统运动方程求解的分离迭代技术和相应的数值解法：对建立车桥系统方程的各种不同方法进行归纳与总结；详细建立了车桥耦合关系，即轮轨接触点处的几何相容条件和静力平衡条件；给出了由于桥梁位移和轨道不平顺而引起的作用在车辆上的轮轨力，以及由于车辆位移引起的作用在桥梁上的轮轨力。

In using integral equation, The author brought forth some new idea about the dissection of magnet. The author also made a thorough investigation and study of the fast convergence numeric algorithm of complete and incomplete elliptic integral. In order to make full use of the computer resource, the author considered the symmetry of the magnet structure.

在应用积分方程法设计时，依据设计要求而对源区进行的剖分有独到之处，并对由剖分而引入的各类完全和不完全椭圆积分的快速收敛数值算法进行了深入探讨，还充分利用磁体结构对称性进行简化，以减少计算时间，使得当前的计算机资源能满足积分方程法之所需。

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。