数值方程

A numerical method for solution of multigroup neutron integral transport equation in two-dimensional hexagonal geometry has been studied in the first part of the dissertation.

本文首先研究了在二维六角形几何情况下，多群中子积分输运方程的数值解法，建立了完整的理论模型及数值方法。

There are many problems can be described by the partial differential equation in the natural science and engineering technology field, studying the numeric solution of these partial differential equations is a strong tool for solving these problems.

在自然科学与工程技术领域中有许多问题都可以用偏微分方程来描述，研究偏微分方程的数值解是解决上述问题的有力工具。

In chapter III,we consider the wavelet method for the approximation of the nu-merical Bergman kernel.It is very clear that the Bergman kernel plays an importantrole in the complex analysis and elliptic equations.The Bergman kernel has a closedrelation with the Riemann mapping,Green function,Neumann kernel and the Szeg〓kernel etc.

第三章研究了数值Bergman核数值逼近的小波方法，Bergman核在复分析和椭圆型方程中占有重要地位，它与Riemann映射、Green函数、Neumann函数、核等有着密切联系。

This paper discusses a kind of nonlinear Sine-Gordon equation and provides a new numerical method for solving the equations.

本文讨论了一类非线性Sine-Gordon方程，并给出了一种新的求解该方程的数值方法。

Based on chapter two, In chapter three, the method of multiple scales is introduced to the study of the multiple-dimensional nonlinear stochastic systems under random external excitation. Using method of multiple scales, we strictly deduce the equation of modulation of amplitude and phase. The effects of random excitations are analyzed; numerical simulations verify the results. Theoretical and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may be changed from a limit cycle to a diffused limit cycle.

在第二章基础上，第三章将多尺度法引入到相应的随机系统的研究中；严格推导了系统的约简方程，用矩方法求出稳态解应满足的方程，获得一些结果；并且数值模拟结果与理论推导的结果是一致的；并注意到，与其对应的确定性系统相比较，系统响应从周期解变为近似周期解，系统的相轨线从极限环变为扩大的近似极限环；随着激励带宽的增大，此扩大的近似极限环的宽度将增大。

The numerical differentiation is often used when dealing with the differential equations.

当求解微分方程问题时，数值微分是常用的方法，将微分方程转化成代数方程组求解。

The above presented methods are applied to solve the 2D harmonic equation. Numerical examples show satisfactory results.

对上述提出的方法，本文以二维调和方程的不同边值问题为例，推导出相应的计算公式，并在随后给出相应的数值算例，数值实验的结果是令人满意的。

In this paper we study the effect of numerical integration in expanded mixed finite element methods for linear elliptic problems.

关于数值积分对椭圆型及抛物型方程有限元方法的影响，已有一些研究，本文考虑了数值积分对扩展混合有限元方法的影响。

Basic equations of seawater intrusion, mathematics models and numerical simulation methods are figured out with the two theories fully studied.

在对咸淡水界面理论有充分了解后，对海水入侵数值模拟研究涉及的基本方程、数学模型和数值方法做了总结。

Moreover, some results about the stability of different numerical methods for the delay system are also itemized.

进一步，又对各种计算方法的数值稳定性进行了回顾，概述了各种常用的数值方法求解延迟微分方程所取得的理论结果。

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。