常微分方程差分解法、入门、多解法.doc

毕业论文 题 目 学 院 专 业 班 级 学 生 学 号 指导教师 二〇一二 年月日【1】 第二部分介绍上述方程的几种差分格式及每种格式的相容性、收敛性与稳定性。 第三部分通过算例检验每种差分格式的可行性。 关键词：偏微分方程；抛物型；差分格式；收敛性；稳定性；算例 ABSTRACT The numerical solution of partial differential equation holds an important role in numerical analysis .Many problems of compution in the field of science and techology include the numerical solution of partial differential equation. For more than 30 years, the theory and method of the numerical computation made a great development and its applications in various fields of science and technology are more and more widely. This paper focuses on the problems based on time. I will use object-constant diffusion equation to introduces the finite difference method of parabolic equation. This paper mainly focus on the basic concept ,basic method and simple numerical example. The first part of this paper introduces partial differential equations and basic concepts of finite difference method.I will introduce the object-constant diffusion equation for the first time. The second part of this paper introduces several difference schemes of the above equation and their compatibility ,convergence and stability. The third part tests the accuracy of each scheme. Key words:partial differential equation；parabolic；difference scheme；convergence；stability；application 目 录 摘要..............................................................………………..................I ABSTRACT………………………………………………………………………...…II 目录…………………………………………………………………………………..……III 1前言……….…………………………………………….….……………………….....….1 2基本概念和定理………………………………………………………………………….2 2.1抛物型方程的基本概念.....……………….………….…………………................2 2.1.1偏微分方程的定义……………………………………………………….…2 2.1.2抛物型方程的定义…………………………………………………….……2 2.1.3初边值条件的定义…………………………………………………….……3 2.2 差分方法的基本思想……………………………………………………..………3 2.3网格剖分....................................................................................................