查询词典 biharmonic equation

We deal with the biharmonic equation and proved that under our assumptions, the week solution of the natural boundary value problem strongly converges (in H~2) to that of the first boundary value problem.

为克服这一困难，我们用具自然边界条件的边值问题(在二阶椭圆型方程情形为第三边值问题)去逼近相应的第一边值问题，并以重调和方程为例，证明了在一定条件下，其具自然边界条件的边值问题的弱解在H~2的意义下强收敛到相应的第一边值问题的弱解。

This paper gives an accurate inversion of matrix of coefficient which is derived fromsolving the boundary-value problem of biharmonic equation in rectangular region by meansof difference method.

将一个n阶电导矩阵实现为具有n+1节点的网络是一很重要的问题，并且引起了广泛的研究，本文扼要地介绍了有关电导矩阵的性质和一些己有的实现方法。

Now we study the properties of four multi-layer potentials and their high deriva-tives of biharmonic equation in the plane when they approach the boundary of adomain.

我们研究了重调和方程四种多层位势及其高阶微商在边界附近的性质，得到了这些微商新的表达式，从而将重调和方程的自由边值问题归化为新的边界积分-微分方程组。

Based on linear bending theory of thin elastic plate and fundamental solution constructed with the general solution principle of biharmonic equation, a meshless method was developed for establishing a computational format of numerical solution of thin plate bending.

基于弹性薄板的线性弯曲理论和重调和方程的一般解理论构造的基本解，建立无网格法求解薄板弯曲问题的数值计算格式。

Firstly, we discuss the boundary value problem of one dimensional biharmonic equation in an interval and its variational problem,multiresolution analysis in the Sobolev space , then solve it with wavelet-Galerkin methods.

首先本文讨论了一维双调和方程边值问题及其相应的变分问题，定义Sobolev空间的多分辨分析，用小波–伽辽金方法进行数值求解，两组基下得到的系数矩阵为七对角阵和块状对角阵。

In Part I, the biharmonic equation are chosen, and the boundary peanlty finite method using piecewise cubic Hermite elements is used to seek their approximate solutions, in particular satisfying the derivative and periodical boundary conditions.

在第一部份里，选择使用片断三次 Hermite元素的边界惩型有限元素法来求解满足边界导数条件和边界周期条件的重调和方程式的近似解。

A semilinear biharmonic equation is studied.

研究了一个半线性双调和问题。

Taking beam with rectangular section as an example, the corresponding analytical solution of beam subjected to cosine distribution pressure is given through constructing the stress function satisfying all boundary conditions and biharmonic equation , which is a base of beam subjected to arbitrary distribution pressure.

以矩形截面简支梁为例，通过构造一个满足所有边界条件和双调和方程的应力函数，给出了梁受余弦分布力作用情况下相应的解析解，这为求解梁受任意分布压力作用下解的问题打下了基础

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

Still based on Ciarlet-Raviart mixed variational principle, this section gives the mixed finite volume element scheme for biharmonic equation on rectangular partition.

综合有限元方法及有限差分方法的优点，李荣华教授于二十世纪八十年代初提出了广义差分方法，亦称为有限体积元方法。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。