求积法

This article derives the extrapolated method gradually from integral action's each kind of optimized model, and it introduces emphatically the Richardson extrapolation technology and the Romberg squaring algorithm.

本文从积分运算的各种优化模型中逐步导出外推法，着重介绍了李查逊外推技术及龙贝格求积算法。

Under the higher-dimensional situation, it introduces mainly the multiple integrals formulas on some standard areas, the multiple integrals formula by the methods of sampling, the reduction of dimensions and the boundary type cubature with a certain algebraic precision, and calculate multiple integrals with the methods of number theoretical net and so on.

在高维情形下，主要介绍了一些标准区域上的多重积分公式，用抽样法来求多重积分，具有代数精度的降维展开式和边界型求积公式，以及用数论网格的方法来计算高维积分等。

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

Under the one-dimensional situation, it introduces mainly the Newton-Cotes formula, the Gaussian quadrature formula, the numerical integration rule of sharp oscillatory function, the numerical integration rule by the methods of sampling and so on.

在一维情形下，主要介绍了Newton-Cotes公式，Gauss型求积法则，急速振荡函数的数值积分法则，抽样法求数值积分的法则等。

Report : Programming Environment : Newton MATLAB7 K polynomial interpolation procedures to achieve Romberg of Quadrature program Gaussian out PCA Elimination of the program.

计算方法实验报告：编程环境：MATLAB7.0 牛顿K次插值多项式的程序实现龙贝格求积公式的程序实现高斯列主元消去法的程序实现。

The author successfully applies the Gauss-type integral formula to the numerical solution to the constant differential equation and creates the Gauss-type implicit Runge-Kutta Method of which the accuracy of order 4 and degree 7 is already equivalent to that of the RK method with order 10 and degree 8 that is in common use.

成功地将高斯型求积公式用于常微分方程的数值解中，得到了高斯型隐式龙格库塔方法，4级7阶 GRK 法的精度已与目前较为常用的10级8阶 RK 法的精度相当。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

Graph paper, parallel, and planimeter methods are current tools for acreage calculation.

目前常用的量算面积方法有方格纸法、平行线法、求积仪法。

In this paper, the domain decomposition method is used for the elliptical boundary problems on a pentagonal region. In every sub-domain, we solve the partial differential equations with TDQ method, namely, triangular differential quadrature domain decomposition method.

为求解五边形上的椭圆型微分方程边值问题，我们借助了区域分裂法(domain decomposition method，简称DDM)，将大区域分成几个小区域，在每个小区域上，用TDQ方法，这种方法我们称之为三角微分求积区域分裂法(triangular differential quadrature domain decomposition method，简称TDQDDM)。

Some typical torsion problems of a cylinder involving a straight,kinked or curvilinear crack were calculated.The obtained results for the case of straight crack...

对圆弧裂纹、曲折裂纹以及直线裂纹的典型问题进行了数值计算，并与用Gauss_Chebyshev求积法计算的直裂纹情形结果进行了比较，证明了方法的有效性和正确性。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。