数值微分

The partial differential equations with singular coefficients are very important ones in the field of numerical mathematics.

摘要具有奇异系数的椭圆及抛物型偏微分方程是一类很重要的方程，早在二十世纪六十年代左右，许多的计算数学工作者就开始研究此类方程的数值方法及相应的数学理论。

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。

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations.

这门研究生程度课程是对微分方程数值解法的应用和理论的高级导论。

Numerical solution of second order differential equations.

二阶微分方程的数值解。

In this thesis we are interested in the stability of numerical methods of delaydifferential equations.

在研究泛函微分方程的数值方法时，稳定性是最重要的课题之一。

Both the results for the numerical stability and the methods used in the stability analysis of the paper are new and valuable.

在随机延迟微分方程数值方法的稳定性研究中，无论是本文中得到的稳定性结论还是分析问题时使用的方法都是全新的，因此具有一定的价值。

has been constructed to solve the delay-differential-algebraic equation, and the numerical stability is also considered.

方法用于求解延迟微分代数方程，并对其数值渐近稳定性作了研究。

3The variables that described changing of gas in the room of gas operatedand moving law of piston are thought random.The numerical value answer aboutrandom differential equation is given.

3考虑描述自动机气筒压力变化规律和活塞运动规律的控制方程中各变量的随机扰动，提出了求解随机微分方程组的数值解法。

The impact of capillary pressure on twophase flow in waterwettish reservoir is studied. The one dimensional control differential equation is derived,and solved by numerical limited difference method.

首先建立一维渗流模型和相应的渗流微分控制方程，用数值差分的方法进行求解，并绘制产量图和采出程度图，分析启动压力梯度和毛管力对水驱油效果的影响。

Here mainly introduces five natures of the initial value problems, In several aspects summed up as the following : whether there are solutions to the problems, whether the only solution, the existence of solutions interval extent; Initial issues under what conditions have a solution--Cauchy - Piano existence theorem; how the district between the definition of a solution to open up a larger interval up; initial value problems for the sole condition --- Lipschitz conditions; 3、the numerical solution of the initial value problems of Ordinary Differential equations .

在这里主要介绍了初值问题的5个方面的性质，分别在这几个方面中总结了以下内容：初值问题是否有解，解是否惟1，解的存在区间有多大；初值问题在什么条件下有解----柯西-皮亚诺存在定理；怎样把在小区间上有定义的解开拓到较大的区间上去；初值问题解的惟1性条件---李普希茨条件；3：常微分方程初值问题的数值解法。

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。