差分方程

By using the difference inequalities, the asymptotic behavior of solutions to forced nonlinear neutral difference equations is studied.

利用差分不等式研究了具有强迫项的非线性中立型差分方程解的渐近性，得到了方程的解趋于零的充分条件

This research method is independent of Green"s function and variational structure. So it can tackle with the BVP for non self-adjoint and self-adjoint difference equations and overcome the difficulties brought about by the establishment of Green"s function, a study of the sign and the estimate of below and above bounded for Greens function.

本章的研究方法既不依赖于Green函数又不依赖于变分结构，因而能解决非自共轭的差分方程边值问题，且克服了Green函数的建立、其符号的判断及其上下界的估计给研究带来的困难，该方法同样适用于研究自共轭的差分方程边值问题。

This model is a group of partial differential equations. Th solution is obtained with finite difference method to give a differential equation of gas pressure, temperature and rate and its calculation step.

该模型是一组偏微分方程，采用有限差分法对其进行求解，给出了计算气体压力、温度、速度的差分方程和详细的计算步骤。

Through the limit difference method,the partial differential equation of the semiconductor device is transformed into a difference equation,and the corresponding boundary condition is discretized with high accuracy.

采用有限差分法把器件工作的偏微分方程转化为差分方程，并将相应的边界条件转化为精度较高的离散化形式。

It is difficult to get the analytic solution of difference equation by using traditional methods with computer.

摘要利用传统方法很难在计算机上实现差分方程的解析解求解，本文提出了一种获得差分方程解析解的线性算法，该算法的基础是完全线形变化法。

In addition, when the nonlinearities have the properties of mixed-monotonicity, the existence of a positive solution for difference equations is ob-tainded by using fixed point theorem in a cone or fixed point theorem of conic expansion and compression.

在最后一部分讨论了带有特征值的非线性二阶差分方程正解存在性问题，利用锥压缩与拉伸不动点定理及逼近性理论，在一定的假设条件下，得到了差分方程正解存在性。

This book reviews the many areas of numerical analysis, including the configuration polynomial, finite difference, factorial polynomials, summation, Newton formula, operator and configuration polynomial, Cheung section, close polynomials, TaylM more item type, interpolation, numerical differentiation, numerical integration, and with the series, differential equations, differential equations, least squares polynomial approximation, minimax polynomial approximation, rational function approximation, triangular approximation, non-linear algebra, linear equations, linear programming, boundary value problems, MonteCarIo methods and so on.

本书综述了数值分析领域的诸多内容，包括配置多项式、有限差分、阶乘多项式、求和法、Newton公式、算子与配置多项式、祥条、密切多项式、TaylM多项式、插值、数值微分、数值积分、和与级数、差分方程、微分方程、最小二乘多项式逼近、极小化极大多项式逼近、有理函数逼近、三角逼近、非线性代数、线性方程组、线性规划、边值问题、MonteCarIo方法等内容。本书的特色主要表现在利用例题及大量详细的题解来透彻地阐明所述内容的内涵，同时附有大量的补充题以便读者进一步巩固和深化从书中获得的数值分析知识。

However, methods and references for difference equation are relatively less. The new method proposed in this paper transfer the complex boundary value problem into the existence and uniqueness of the solution of the linear equations. For linear case , we obtained the necessary and sufficient conditions for the existence and uniqueness of the solution for the BVP; For the nonlinear case ,we got a series of new sufficient conditions by using contraction mapping theory and cone theory .

而差分方程边值问题的研究方法和文献还很少，文中新的研究差分方程边值问题的方法是将复杂的边值问题求解转化为代数理论中的线性方程组解的存在和存在唯一问题；对线性情形，较容易地获得了边值问题的解存在以及唯一的充分必要条件，而对非线性情形，则通过压缩原理和锥理论等各种不动点定理，获得了一系列新的充分条件。

Chapter 2, we investigate the existence of multiple positive solutions of the neutral partial difference equations on the base of the existed results of partial difference and difference equations, and obtain some sufficient conditions for the existence of multiple positive solutions.

第二章，基于已有的偏差分方程和差分方程的结果，我们研究了高阶非线性中立型偏差分方程多正解的存在性问题，建立了判断多正解存在的充分条件，对前人的结果进行推广。

Based on Wu's elimination method and "divide-and-conquer" strategy, the undetermined coefficient method for constructing polynomial conservation laws of nonlinear differential-difference equations was improved. Furthermore, a Maple package CLawDDEs was developed to automatically derive conserved densities and associated fluxes of polynomial differential-difference equations.

基于吴消元法和"分治"策略，改进了基于标度不变性构造非线性微分差分方程多项式形式守恒律的待定系数算法，并在计算机代数系统Maple上实现了改进后的算法，其中的软件包CLawDDEs可自动推导出微分差分方程的守恒密度及连带流。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。