查询词典 galerkin equations

In the two-dimensional simulation, the fully implicit difference scheme is used for the continuity equations to ensure numerical stability; Jacobian iteration is used to solve the difference equations, and only nonzero elements in the coefficient matrixes of these equations are dealt with, which reduce the requirement for memory and shorten the calculation time.

在两维模拟计算中，对连续性方程采用全隐式差分方案以保证数值稳定性；运用雅可比迭代法求解差分方程组，并且在求解过程中，只对差分方程组系数矩阵中的非零元素进行处理，因此减少了对内存的需求量，而且缩短了计算时间。

Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcame. Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations.

边界方程有多种选择，在选定一种边界方程的基础上，可以通过建立一个新的边界方程来表示问题的边界，以克服积分核的奇异性；最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

Green quasifunction method is applied to Poisson's equations. Fredholm integral equations of the second kind are obtained. Irregularity of the kernel of integral equations is overcome by choosing a suitable form of the normalized boundary equation.

应用准格林函数方法，可将Poison方程化为第二类Fredholm积分方程，通过边界方程的适当选择，积分方程核的奇异性被克服了。

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

At first, the governing differential equations are solved by Fourier transform, then, under consideration of the mixed boundary value condition, a pair of dual integral equations about the vertical vibration are listed which are converted to linear algebra equations by the Jacobi orthogonal polynomial and solved by numerical procedures. Consequently, the dynamic compliance coefficient Cv versus the dimensionless frequency is derived, and the program is compiled.

首先，采用Fourier积分变换解析求解了Biot方程，得到了该动力控制方程在Fourier变换域上的一组通解，然后由混合边值条件建立了地基上基础竖向振动的对偶积分方程，并应用Jacobi正交多项式将其转化为一组线性代数方程组，通过求解得到了不同无量纲频率下基础振动的动力柔度系数Cv，编制了相应的计算程序。

Rumjantsev used Hamilton's principle with Lagrange's multipliers to generate the dynamical equations of a rigid-fluid coupled system in 1954 and the dynamical equations and their dynamical boundary conditions of a fluid-elastic coupled system in 1969, where the fluid is incompressible and inviscid. In 1990, Liu used Jourdain's principle with Lagrange's multipliers to generate the dynamical equations of a rigidfluid coupled system, where the fluid is incompressible and viscid.

Rumjantsev利用带Lagrange乘子Hamilton变分原理于1954年建立了刚—流耦合系统的动力方程，于1969年建立了流—弹耦合系统的动力方程及其动力边界条件，其中所考虑的流体是不可压无粘液体；Liu利用带Lagrange乘子Jourdain变分原理于1990年建立了刚—流耦合系统的动力方程，其中所考虑的流体是不可压粘性液体。

The dynamical equations of a liquid-filled tank were deduced using Jourdain principle,including the momentum and angle momentum equations for the coupling system and Navier-Stokes equations for the liquid sloshing.

液体模块采用Lagrange-Euler描述方法建立有限元计算模型；充液刚体模块利用二阶显式Runge-Kutta格式离散的常微分方程组。

On the basis of classical lamination theory and large deflection hypotheses of plate, the equilibrium and compatibility equations of simply supported composite laminated plates were obtained. The nonlinear partial differential equations are transformed into the ordinary differential equations of Kronecker tensor product by series expansion and solved numerically by the fourth-order Runge-Kutta method.

基於经典的层合板理论及板的大挠度基本假设，得到四边简支层合板的非线性运动方程及变形协调方程；用级数展开把非线性偏微分方程组化为易於求解的Kronecker张量积形式的二阶常微分方程组，并由四阶Runge-Kutta法数值求解。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

We calculate the differential characteristic set of determining equations for source evolution equations (include several linear and nonlinear differential system of equations).

用算法′计算了几个微分方程对称的确定方程组(包括线性微分方程组以及非线性微分方程组)的微分特征列集，并在计算量上对算法′与算法进行了比较。

After oxidation, pH value of the surface of carbon black has a specific relation with the volatile content.

氧化后炭黑表面的pH值与挥发分之间有一定的关系。

Knowing that such a person is warped and sinful; he is self-condemned.

因为知道这等人已经背道，犯了罪，自己明知不是，还是去做。