查询词典 galerkin equations

Based on the Galerkin Method the variational problem for the point source 2.5-dimensional electricfield is derived and the corresponding finite element equations are obtained.

基于Galerkin法推导了点源2.5维电场的变分问题，得到了对应的有限元方程组。

Insection 4.3, semi-discrete and fully discrete Fourier spectral and pseudo-spectral schemes are constructed. The convergence and stability for the schemes are proved, and the error estimates are obtained.Chapter 5, consider the damped coupled generalized nonlinear wave equations. In section 5.2, by coupled a priori estimates and Galerkin method, prove the existence and uniqueness of the global smooth solution for the periodic initial value problem and obtain the existence of global attractors.

第四章，考虑一类具耗散的广义KdV方程组的周期初值问题，在第二节中证明了整体光滑解的存在性和唯一性，得到整体吸引子；在第三节中构造了半离散和全离散的Fourier谱格式和拟谱格式，在整体光滑解存在的条件下，证明了这些格式解的收敛性，并得到了误差估计。

A detailed model of non-linear parametric excitation vibration coupling the stay cable and the girder, in which the static sag as well as the geometric non-linearity are considered, is proposed in this paper. Based on several numeric examples investigated by the Galerkin method composed with the integration strategy, several kinds of factors effecting stay cable parameter vibration are studied. Another parameter vibration model by the axial excitation is presented and the corresponding nonlinear equations are derived. The smallest excitation amplitude,the transient state and steady state resonance amplitudes, and the changing characteristics of the axial force are obtained by using harmonic balance method. According to numerical examples calculated by numerical integration method, the effects of the inner damping of the stay cables are investigated.

本文创新地提出了斜拉桥拉索-桥面耦合参数振动模型，推导了索-桥耦合非线性参数振动方程组，联合Galerkin法及数值积分方法，对各种特性的拉索进行了数值求解，得出了影响拉索参数振动的各种因素；提出了斜拉索受轴向端激励参数振动模型，导出了模型的非线性振动方程，使用谐波平衡法得出了产生参数振动需要的最小激励幅值、共振时瞬态及稳态的振动幅值及索拉力的变化特性，并用数值积分方法对实际斜拉桥拉索进行了计算，分析了拉索阻尼对参数振动的影响。

Nonlinear partial differential dynamic equations of bending vibration of a tilting stepped drive shaft with two supports were built under non-inertia movement coordinate system by theorem of the motion of mass center and Heaviside function. According to the condition of equal displacement in an adjoining plane of the shaft, an equivalent shaft and its equation were obtained. A motion equation of the equivalent shaft was obtained by method of Galerkin. An approximate steady-state solution of the main resonance was obtained by method of multiple scales. The influence factors, motion stability, amplitude jump of main resonance of a stepped drive shaft and so on were analyzed.

用质心运动定理、Heaviside函数建立了非惯性系下倾料两端支承阶梯传动轴的非线性弯曲振动偏微分动力学方程，并根据相邻轴段的衔接面处位移相等的条件，得到阶梯轴的当量轴及其动力学方程；用Galerkin法得到当量轴的弯曲运动方程，用多尺度法求得稳态下当量轴的主共振的一次近似定常解，分析了影响阶梯传动轴主共振的因素、运动稳定性、振幅突变性等。

The stream function equations are derived, based on the fluid equations of motion on a revolving S 1 stream surface in centrifugal pump impeller, for indirect boundary element method. The equations are suitable ideal and incompressible fluid flow with rotation or non rotation in absolute coordinate system.

根据离心泵叶轮S1流面的流体运动方程，推导了间接边界元法所需的流函数方程，它适用于不可压理想流体的绝对流动有旋或无旋流动。

The basic idea is to set a continuous solution of the region with a finite number of discrete points instead of a grid consisting of, these discrete points called grid nodes the solution of a continuous area on a given function of continuous variables used in the definition of discrete grid variable function approximation the original equation and boundary conditions in the micro-business operators to approximate differential, integral with the points and to approximate, so the original differential equations and boundary conditions are replaced by algebraic equations near Side, that is, finite difference equations , solve this equation group can get the original problem in discrete points on the approximate solution.

基本思想是把连续的定解区域用有限个离散点构成的网格来代替，这些离散点称作网格的节点；把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似；把原方程和定解条件中的微商用差商来近似，积分用积分和来近似，于是原微分方程和定解条件就近似地代之以代数方程组，即有限差分方程组，解此方程组就可以得到原问题在离散点上的近似解。

It can be extended to solve partial differential equations with higher order such as KdV equations and biharmonic equations.

该方法可以推广到更高阶的方程，如Korteweg-de Vries方程、重调和方程等。

In addition, we note that the Newton limit of the relativistic hydrodynamics equations is the classical compressible fluid Euler equations system. This is one of the motives that we research the relativistic hydrodynamics equations.

此外，我们注意到相对论流体力学方程组的Newton极限即为经典的可压缩流体力学Euler方程组，这也是我们研究相对论流体力学方程组的动机之一。

Derive the equations of continuity by using the method of infinitesimal based on the mass balance equations and the differential equations of gas and oil phase fluid flow.

再根据物质平衡原理，利用微元法分析凝析油气渗流规律，建立连续性方程，从而导出凝析油气渗流微分方程。

This course offers advanced topics for students who have learned ordinary differential equations. The course includes linear algebra which has topics as matrices, linear systems of equations, eigenvalue problems, vector differential and integral calculus. Fourier series, orthogonal functions, Fourier transforms and partial differential equations will also be introduced.

本课程为提供已有常微分方程式基础的同学修习，内容包括线性代数，矩阵运算，特徵值问题，向量的微分与积分，一阶线性微分方程组，傅力叶级数和正交函数，傅力叶转换，并将对椭圆，抛物线，双曲线型式的偏微分方程式作概略介绍。

"Please accept this talisman as a token of our thanks."

请收下这个护身符以表达我们的感谢。

If I have that magic, I will be more acceptable in the society.

如果我拥有那种魔法，我将更加被这个社会所容纳。