求积公式

The quadrature formula about surface integral on any quadrilateral element is deduced by means of isoparametric transformation and bilinear interpolation.

通过对三维有界区域的边界曲面作四边形网格剖分，用有限元方法处理高斯公式中的曲面积分，由等参变换及双线性插值导出任意四边形单元上曲面积分的数值求积公式。

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。

The author of this text has put out a kind of new-type quadrature formula by using the Gaussian quadrature formula and the orthogonality of Per Kai polynomial.

应用Gauss型求积法则和Per Kai多项式的正交性质，本文作者推导出了一种新型的求积公式—Gauss-Per Kai积分公式。

According to a given function, namely, composite trapezoidal formula using composite Simpson formula Romberg quadrature formula and the variable step-size integration quadrature formula results, and compare the accuracy of points.

详细说明：根据给定的函数，分别用复合梯形公式、复合辛普森公式、龙贝格求积公式和变步长的求积公式计算积分结果，并且比较积分的精确度。

We proposed theautomatic and semi-automatic inverse Laplace transform methods and acriteriar for the optimal choice of transform parameters.24 numerical inverseLaplace transform formulas are compared for 16 different problems that haveexact solutions.

利用流行的数值积分方法，如Newton-Cotes求积公式、Gauss求积公式和振荡函数求积公式，共构造了24种Laplace逆变换方法。然后以16个有工程应用背景的Laplace逆变换问题为例，比较了这24种方法的优劣，得到了一些新的结论。

Plot --- composite numerical quadrature formula to solve the problem of integration functions for composite tr...

数值积---复合求积公式对积分问题的求解功能用复合梯形求积公式和复合抛物线公式，对给定的积分问题进行计算。

Plot --- composite numerical quadrature formula to solve the problem of integration functions for composite trapezoidal plot formula and compound parabolic formula, the right to issue integral calculation.

数值积---复合求积公式对积分问题的求解功能用复合梯形求积公式和复合抛物线公式，对给定的积分问题进行计算。

As using Gaussian numerical integration, this paper uses Gauss-Legendre quadrature formula instead of Gauss-Chebyshev quadrature formula in order to avoid the precision decrease due to the singularity of cut-off error at both end points.

在利用高斯型求积公式进行数值积分时，本文采用高斯—勒让德求积公式取代高斯一切比雪夫求积公式，以避免因截断误差在端点出现奇异而导致的精度下降。

In the third chapter, the contractilities and asymptotical stabilities of neutral delay integro-differential equations are concerned. The extended Runge-Kutta methods, with the compound quadrature formula and the Pouzet quadrature formula, are numerically stable under suitable conditions. The numerical experiments prove this result.

第三章，研究了中立型延迟积分微分方程，其理论解的收缩性和渐近稳定性，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，并获得了数值方法的稳定性条件，随后的数值试验结果进一步证明了方法是数值稳定的。

In the second chapter, generalizing the contractilities and asymptotical stabilities for multi-delay integro-differential equations. Under proper stepsize, we obtain the discretization schemes of Runge-Kutta methods with the compound quadrature formula and the Pouzet quadrature formula, and besides, derive the global and asymptotical stabilities. Moreover, the numerical experiments show that the presented methods are highly effective.

第二章，考虑了多延迟情形下的积分微分方程，推广理论解的收缩性与渐近稳定性结果，在适当的步长下，利用复合求积公式与Pouzet求积公式扩展Runge-Kutta方法，获得离散的计算格式，并且证明了方法是数值稳定的，此外，数值试验表明此计算方法在实际应用中是非常有效的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。