逼近

The boundary value problem for first-order differential equations with a parameter refers to the finite solution condition of equation which includes unknown quantity and its first-order derivative that not only relies on interval value but also relies on the parameter of the equation,which is always settled by fixed point theory or successive approximation method.

含一个参数的一阶微分方程边值问题是指：含有未知量及它的一阶导数的方程的定解条件不仅依赖于在区间端点的取值，而且依赖于方程中的参数。通常它用不动点定理或逐步逼近法来解决。

Numerical differentiation is that derivative value of a function at a certain point is approximately solved in discrete method.

中文摘要：数值微分就是用离散方法近似地求出函数在某点的导数值，关于数值微分已有许多求解方法，但这些方法都有各自的局限性，并且关于高阶导数近似逼近的方法研究相对较少。

We also give some conservation and convergence analysis for the Dirac equation and the Korteweg-de Vries equation.

在第七章中，我们建立了全直线上不带权的Legendre有理谱逼近，并以Dirac方程作为实例，证明了谱格式的守恒性和收敛性。数值结果表明了算法是有效的。

The solution of some practical problems in engineering can be regarded as that of periodic solution of nonlinear autonomous systems according to the opinion of mathematics, The problems of this kind are analysed by means of the direct numerical method in this paper,The simple and convenient Draw Newton Method is applied for solving the parameter vectors in iteration course along with the calculation of a practical engineering problem.

日I崖旨J，'口工程中的一些实际问题往往可以归结为非线性自治系统，例如描述同步发电机暂态稳定性问题的转子摇摆方程，即是一典型的非线性自治系统。虽然可以用各种小参数摄动法求解非线性系统，但是这类方法是依据对线性系统的解进行"摄动"来逼近非线性系统解的。因而当系统

However, to establish global convergence for these latter methods, one must enforce either sufficient decrease conditions (the Armijo-Goldstein-Wolfe conditions)or a fraction of Cauchy decrease condition - all of which rely on explicit numerical function values, as well as explicit approximations to the directional derivative at the current iterate.

但是，为了保证后面方法的全局收敛，必须有足够的减少条件（Armijo-Goldstein-Wolfe条件）或者部分柯西减少条件——它们全都依赖于外在的数值函数值，就和在当前迭代逼近方向导数一样。

Numerical experiments show that, with increasing the number of unit cell, n, the results got from RVE method under the Dirichlet and Neumann boundary conditions converge towards those the obtained by the homogenization method from the upper and lower sides respectively.

数值结果表明，Dirichlet型和Neumann型边界条件下的代表体元法所得结果随着参与模拟的单胞个数的增加，分别从上下界逼近均匀化方法的结果。

This paper is devoted to the existence and multiplicity of the solutions of the homogenous Dirichlet problem for a nonlinear singular elliptic equation with natural growth in the gradient.

研究一类具奇性和退化性的非线性椭圆方程Dirichlet问题，通过构造适当的逼近问题并结合紧致方法，证明了解的存在性和多重性。

The kernel is adding a discontinuous function for the standard approximation to account for the crack. A feasible technique is adopted for dealing with multiple cracks and intersecting cracks.

本文研究扩展有限元方法，通过改进标准有限元的单元逼近函数，使之能够表达单元内的几何不连续，从而实现切割和断裂的模拟。

The artist herself describes how to approach her work:"The more every single recipient intrudes into this picture world - consciously and subconsciously - the clearer it gets that terms like discrepance, ambivalence and ambiguity match the work more than consistent interpretation."

艺术家是这样描述她作品的欣赏方法的：当受众越逼近这个图片世界时，无论是有意识的还是无意识的，他会更清晰地感受到'差异'、'矛盾心理'、'含糊不清'这些词比持续不断的分析解释更适合该作品。

In this paper,the authors give a strict proof of geometric Brown motion displayed by stock prices using the methods of approximation from discrete process to continuous stochastic process.

通过由一般的离散过程逼近连续随机过程的方法，给予证券价格按有漂移率的几何布朗运动变化的一个严格的证明，并指出了股票价格过程的一般模型

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。