查询词典 evolution equation

In the computation of aerodynamic forces, the present work is based on the work of Morino et al., but the following aspects are improved:(1) In computing the steady transonic aerodynamic load, the steady transonic nonlinear integral equation is solved by relaxation-iteration method in this thesis, instead of solving the time dependent transonic nonlinear integral equation, so that the computing time is saved greatly;(2) The influence coeifficients represented by volume integral are transformed to surface integral by using the Gaussian Theorem, so the analytical form of these coeifficients can be obtained and this leads to be more convenient to analyse and compile computer program;(3) The shock capturing method is used in every time step in present work, no shock moving term is added in the integral equation, so that it is more convenient and simpler to treat.

在气动力计算方面，本文基于Morino等人的工作，作了如下几方面的改进：（1）在计算定常跨音速流场（作为非定常绕流计算的初场）时，本文采用松驰迭代法直接求解跨音速定常非线性积分方程，而不是采用时间相关法求解非定常非线性积分方程，这样大大节省了计算机时；（2）将以体积分形式出现的影响系数化为面积分，并获得解析公式，这样便于分析和编写程序；（3）对运动的激波，本文通过在每一个时间步长上采用激波捕捉法而得到，而不是在积分方程中附加激波运动项，因而处理起来简单方便得多。

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。

From K-G Equation and Dirac equation,using 2-D invariant line element, the radius equation and event horizon formula of particles are obtained.A simpler method to the research of quantum effect of the scalar and vector particles in black hole with spherical symmetry is singgested.

分别从K-G方程和Dirac方程入手，利用简化后的二维不变线元，直接给出了粒子的径向方程和视界面方程公式，为研究球对称黑洞中标量粒子和矢量粒子的量子效应提供了一个更简单的方法。

Based on the transformation between position space and spinor space in geometric algebra system,the perturbing Kepler equation was transformed to a linear and regular form(also called Kustaanheimo-Stiefel equation or KS equation).

利用几何代数体系中的位置空间与旋量空间之间的转换关系，将摄动Kep ler方程转化为线性、正则的旋量方程，并给出Kep ler旋量方程的解。

Wave equation, heat conduction equation and Laplace's equation are the second-order linear equations.

波动方程、热传导方程和拉普拉斯方程都是二阶线性方程。

It starts from the Laplace equation of a two-phase interface, to the Young equation of three-phase contact line, as well as some modifications on the Young equation appeared in literature.

文章从介绍二相界面的Laplace方程开始，到Young提出的关于三相接触线的平衡方程，以及后来的一些研究者对其做的修正补充。

Governing equation s adopted are Stokes equation for momentum and Laplace equation for energy.

由于研究对象是小液滴缓慢的热毛细迁移过程，因而所采用的控制方程中动量方程为StokeS方程、能量方程为Laplace方程。

Making use of the fundamental solution of Laplace equation, we change the nonhomogeneous Helmholtz equation with veriable coeffients into integral equation.

利用Laplace方程的基本解，将变系数非齐次Helmholtz偏微分方程的边值问题化为积分方程问题。

First the topological relations between the unknown points and known points are built as a linear constrain, then the DSI equation group is formulated by combining Laplace equation with the linear constrain equation.

首先由待插值点与已知点之间的拓扑关系建立线性约束，进一步结合位元场满足Laplace方程，建立离散光滑插值联立方程组，采用预条件共轭梯度求解该方程组。

By the least common denominator of all denominators in the equation to transform it into an integral equation;（2）Solve the integral equation

一次函数y=kx+b有下列性质：当k＞0时，y随x的增大而增大，这时函数的图象从左到右上升：当k＜0时，y随x的增大而减小，这时函数的图象从左到右下降。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。