问题求解

In this paper, propose a new method based on the MATLAB/PDETOOL Box to solve the definite solution problems for elliptic equation problem, and the needed time of the program for the different nodes.

基于有限元的MATLAB/PDETOOL工具箱库函数，对MREIT中的椭圆方程定解问题进行数值求解，还给出了求解规则区域的定解问题时，不同节点所需的运算时间。

In this paper, we construct the differential equation to solve the unconstrained optimization problem. Such methods solving the ill-conditioned problems are very effective. It indicates that the asymptotically stable region of explicit the Euler method to solve the differential equation equals to the descent region of the gradient method to solve the original unconstrained optimization problem.

我们发现，在用Euler方法求解二次优化问题的等价动力系统的方程时，由方法的步长确定的稳定区域对应于这些方法所得到的迭代公式的步长满足单调下降算法的条件确定的单调下降区域，因此我们可以利用这个性质构造解无约束优化问题的数值方法而不采用标准的常微分方程的数值求解公式。

This paper extends the ant colony algorithm which is used for solving 0-1 knapsack problem in reference [7], and gets enlightenment from the ant colony algorithm with 2-opt local optimization for solving traveling salesman problems: Exchange strategy can make the algorithm have faster convergence rate and get better quality solution. So this paper presents the ant colony algorithm based on exchange stragegy.

本文推广了文献[7]中求解单维0-1背包问题的蚁群算法，并从结合2-opt等局部优化的蚁群算法求解旅行商问题中得到启示：通过交换策略可以加快算法的收敛速度和获取更高质量的解，因此提出了基于交换策略的蚁群算法。

In the second part,we have mainly discussed the error es-timates of the numerical methods for solving ill-posed problem,including the error estimate of finite-dimensional regulariza-tion method in Chapter 5,and the error estimate of regulariza-tion-spline method for solving Fredholm integral equation ofthe first kind.

在第二部分，我们主要讨论了不适定问题数值方法的误差估计，包括有限维正则化方法求解不适定问题的误差估计以及用样条正则化方法求解第一类Fredholm积分方程的误差估计，两者均是目前还未有的结果。

In this paper, the scattering of SH wave by the structure surface with multiple semi cylindrical medium inclusion is studied by using a function of complex variable and a multi polar coordinate method .

利用复变函数和多极坐标系的方法，研究了在结构表面上含有多个半圆形介质夹杂的散射问题，首先给出 SH波对多个半圆形介质夹杂的散射波函数，并利用多极坐标系的方法，来满足介质界面上的连续条件和表面上的边界条件，归结为对一组无穷代数方程组的求解，简化了问题的求解。

In this paper,an algorithm to find the initial solution of linear programming is provided.

本文给出了一个求解线性规划问题初始解的算法，该算法是将作者原算法稍加修改而成，与原算法配套组合，即构成一个完整的求解一般线性规划问题的强多项式算法。

The results of experiments show that the neural network algorithm solving differential equations with the initial value problem can establish mathematical model, which can be calculated any given point of function, which is any difference method can not do.

针对微分方程初值问题的求解，论文探索性研究了求解微分方程初值问题的神经网络模型算法，并分析了算法的收敛性，为神经网络学习率大小的确定建立了理论依据。

This internal fault simulation is a typical stiff system and the stiff integration method with variable step-size and order are applied.

内部故障仿真求解是典型的非线性刚性微分方程问题，需采用变步长的适合求解刚性问题的算法。

Stokes problems of interior domain are discussed synchronously, and comparied with pure numerical method.

3采用自然边界积分与有限差分的耦合方法，求解了自然边界积分法无法直接求解的一般区域上的Stokes问题，探讨了内部区域Stokes流问题，并与纯数值方法的结论作了比较。

Special attention should be paid when we apply the decomposition method to two-point boundary value problems, it is necessary to solve a algebraic system;It should be noted that a modification of inverse operator should be made when dealing with singular boundary value problems;Laplace transform and Pade approximants can be coupled to enhance the efficiency of the decomposition method.

比如，在求解两点边值问题时就需要特别注意，这时需要采用待定系数法，最后会涉及到系数方程组的求解；在处理奇异边值问题时需要重新定义逆运算；不少研究人员还把分解方法与Laplace变换和Padé逼近相结合来进一步提高分解方法的精度。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

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