偏微分方程的积分法

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

The coefficients in trial function can be gained by the point collocation method, then the solution of the boundary value problems is obtained. Non - uniform beams and irregular plates on Winkler foundation and plates on elastic half space foundation can be numerical calculated by the introduced method.

为对土与结构物的相互作用进行研究，在采用适当的土体模型的基础上，必需求解地基与基础的共同作用方程，而该共同作用方程一般是偏微分方程或微分积分方程，除一些简单的模型外，其解析解较难获得，因此只能采用数值方法求其结果，加权残仇法是一种L作鼠少、简便易行的数仇方法{2，但其解的精度'。

The governing equation of in-plane vibration of cable-restraint system is derived by means of D'Alembert principle, and then those partial differential equations are transformed into a set of ordinary differential equations by Garlerkin method. The method of Runge-Kutta integration is applied to solve the equation. The simulation analysis is made to prove that this vibration control has obvious damping effects and then the influence of cable tension, support mass, natural frequency and spring stiffness on the damping are discussed. Eventually, the approximate analytic solution of the optimum damping parameter is obtained to provide a simple and effective reference and design method for the engineers.

通过D'Alembert原理建立拉索－弹性约束系统振动方程，通过Galerkin方法将偏微分方程转化为常微分方程，应用龙格－库塔积分法求解方程；经过仿真分析，验证了该振动控制具有明显的减振效果，并且讨论了初始拉力、支座质量、振动频率及弹簧刚度对减振效果的影响；最后给出了计算最优阻尼参数的近似解析式，为工程师提供了简便有效的参考依据及设计方法。

Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.

其次，由于无网格法的近似函数不是插值函数，所以无网格Galerkin法在处理边界条件和对区域积分时是不同于有限元的，它有其独特的处理方法，从加权残量法——Galerkin出发，推导出抛物型偏微分方程无网格Galerkin法的基本方程，并对影响无网格Galerkin法的主要因素进行探讨，给出了取得最佳效果的相应建议。

Jacobian Davis iterative method of solving equations AX = B, least squares polynomial fitting, portfolio Simpson formula for integration, with a triangular decomposition method of solving equations AX = B.

拉格朗日插值多项式拟合，牛顿插值多项式，欧拉方程解偏微分方程，使用极限微分求解导数，微分方程组的N=4龙格库塔解法，雅可比爹迭代法解方程AX=B，最小二乘多项式拟合，组合辛普生公式求解积分，用三角分解法解方程

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。