平均方法在差分方程中应用的研究.doc

本科学生毕业论文 平均方法在差分方程中应用的研究 系部名称： 专业班级： 信息与计算科学 学生姓名： 指导教师： 职 称： 黑 龙 江 工 程 学 院 二○一○年六月 The Graduation Thesis for Bachelors Degree Average method in difference equation application research 摘 要 本文主要研究了平均方法在差分方程中的应用。在遍历函数的基础上，引入了遍历序列的概念。然后从两方面研究离散情况下的遍历问题，从中得到了一些遍历序列的性质，在离散情况下主要应用平均方法得到了动力系统的解的定量性质。 本文首先介绍了动力系统的背景以及发展情况，然后介绍了动力系统与差分方程之间的关系。主要从两方面研究动力系统，从实际出发，动力系统不仅有连续的情况，也有离散的情况。因此，我们首先证明了在连续情况下定理的成立，从而得知在离散的情况下定理仍然成立。接下来在初值问题中证明得到了相关结论。 动力系统理论与分方程定理论中所探讨的内容似无多大的区分，然而有不同的侧面动力系统着重在抽象系统而非具体方程的定性研究，其研究办法着眼于一族轨线间的相互关系，换言之，是整体性的。这整体性有些是拓扑式的,也有些是统计式的后者主要是遍历性。动力系统理论是经典常微分方程式论的一种发展。ABSTRACT In this paper, the averaging method is used into dealing with the difference equation. On the base of the ergodic function, we give the definition of the ergodic sequence. The study of the ergodic sequence consists of two parts. One is the properties of the ergodic. The other is using the averaging method to deal with a quantitative aspect of a difference equation in dynamical system. At first, we introduce the background and the develop of the dynamical system. And then we get the relationship from the difference equation and the dynamical system. In fact, the study of dynamical system consists of two parts. One is continuous. The other is discrete. Therefore, we first prove theorems in the continuous case. So that, in the case of discrete theorems still hold. Then the proof obtained the related conclusion in the initial-value problem. Dynamical systems theory and differential equations in the quantitative theory of content seems of little distinction, but have different side. Dynamic system emphatically in abstract system, but the non-concrete equations qualitative investigation, its research means focus on a race gago line between the reciprocity. In other words, it is comprehensive. This is the topological integrity of some type, and also some statistics-based; The latte