多步法

The first part in this dissertation is about multistep discretization of DAEs.

本文介绍的第一个方面是求解微分代数方程的多步法公式。

Compared with standard Crank-Nicholsonscheme in the same computational time and resource, the method has two characteristics: small truncation error of in the transverse direction and high accuracy. It is a useful tool for designing optical waveguide devices.

与标准格式的有限差分光束传播法相比，该算法在几乎不增加计算时间和计算机内存资源的情况下，结合了道(来源：122eA22BC论文网www.abclunwen.com)格拉斯格式的有限差分光束传播法截断误差小和宽角多步法所具有较高精度的优点，是光波导器件理想的数值模拟工具。

Secondly,the one-step and multistep methods of the precise integration algorithms arederived by means of the integration of functional matrix by parts and interpolation function,and some recursion schemes suitable for precise integration are obtained.

然后，以函数矩阵的分部积分法和插值函数为工具，推导出精细积分的单步法和多步法，给出了多种精细积分的递推格式。

A new nonlinear multistep method is constructed based on the implicit Euler method in this chapter, named Schur product multistep method.

本文在隐式Euler方法的基础上构造了一种非线性多步法，即Schur积多步方法。

A non-stiff transformation method is presented in this paper, based on the above theory, general Schur product multistep method is put forward.

本文讨论了刚性常微方程的非刚性转化方法，在此基础上，获得一类广义Schur积多步法（通过这种非刚性转化方式，显式Euler方法将成为一个A-稳定的方法）。

In Chapter 3, we investigate the delay-dependent stability analysis of linear multistep methods when they are applied to the neutral delay differential equations. We state a necessary condition for any linear multistep method applied to the neutral delay differential equation to be Nτ(0)-stable.

在第3章中，考虑了中立型延迟微分方程线性多步法依赖于延迟的稳定性分析，给出了任意线性多步法是Nτ（0）-稳定的一个必要条件。

The properties of the general linear multistep method for piecewise smooth dynamics of mechanical systems are analyzed and a picewise smooth vibration model is introduced. Some numerical experiments on the vibration model are made and several improved integration methods are presented.

采用Taylor级数展开方法，分析了常用的线性多步法在非光滑机械动力系统中的计算精度特性，建立了一个非光滑的机械振动系统检验模型，给出了典型的计算实例，并提出了几种改善计算精度的措施。

It is proved that if the RungeKutta method and the linear multistep method are of order p, then the numerical Hopf bifurcation value is an approximation to the Hopf bifurcation value of the equation itself of the same order p.

证明了如果Runge-Kutta方法和线性多步法是p阶的，那么数值Hopf分支值以相同的阶数p逼近于方程本身的Hopf分支值。

An improved Schur multistep method has been presented for controlling error severely cumulating and increasing computational accuracy.

为解决刚性问题中导函数项的"病态性"（导函数中同时含有较大参数和较小参数），本文提出了一种改进的Schur积多步法，数值实验表明，该方法能很好地抑制误差的急剧累积，与原方法相比，计算精度得到较大提高。

The synthesis of hyperbranched poly based upon 1,2-bis diallyl (methyl silyl ethane (B4) as a core molecule and diallyl silane (AB2) monomer via hydrosilylation addition have been investigated: And the hyperbranched poly were prepared using onestep without core, one-step with core and pseudo-one-step methods.

以四烯丙基硅烷(B4)为核、甲基氢二烯丙基硅烷(AB2)为单体，通过硅氢加成反应，采用无核一步法、核一步法、核多步法合成了超支化聚有机硅破烷。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。