求积法

Two types of new Abel differential equation are structured by method of variation replacement, variation position transformation and compound function derivation law.

借助变量替换法、交换变量位置法及复合函数求导法则，构造出两类新的 Abel型微分方程，论证它们的可积性，提供可积的判据，从而推广有关文献的结论，扩大微分方程的可积范围。

According to the variation, features of the integrand, the values of peaks and troughs are taken out and formed a slowly convergent series, and the repeated averaging scheme is performed to calculate the limit rapidly and accurately.

根据被积函数的变化特点，将波峰和波谷值抽取出来组成慢收敛序列，利用重复平均法快速而准确地求出其极限值。

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用"去行去列法"和"置大数法"进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

Report : Programming Environment : Newton MATLAB7 K polynomial interpolation procedures ...

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。

Proceeding by Bubnov-Galerkin method in combination with numerical method based on the quadrature formula the problem was reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.

根据Bubnov-Galerkin法，结合基于求积公式的数值方法，将问题简化为求解具有松弛奇异核的非线性积分－微分方程的问题。

In traditional reservoir capacity calculation, a planimeter is used to obtain a reservoir capacity from topographic maps and large scale topographic maps are needed if high accuracy is required.

传统的库容计算方法是在已有的地形图上采用求积仪法进行，当精度要求较高时，需到现场实测更大比例尺的地形图。

Reserves ; volumetric method ; planimeter ; boundary ; area

地质储量；容积法；求积仪；边界；面积

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用&去行去列法&和&置大数法&进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

An important method for evaluating integrals is a change in variables .

求积分值的一种重要方法是变量代换法。

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

详细说明：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。

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。