摘 要
常微分方程是研究许多自然科学问题和技术问题的有力工具，因而具有重要的实用价值；它在力学、天文学、物理学中，在许多化学和生物学问题中，有着广泛的应用。这是因为大量现象、过程所服从的客观规律往往能够写成常微分方程的形式，因此这些方程本身就是相应客观规律的定量表示。常微分方程的初值问题和边值问题计算都是常微分方程的基本计算之一，贯穿于常微分方程的始终。生产实际问题多数是初值问题和边值问题，本文旨在对常微分方程的初值问题和边值问题进行分类汇总，达到对初值问题和边值问题的求解的较为细致的总结与探讨。本文对常微分方程的初值问题和边值问题的解法进行了归纳总结，从其性质出发，进行了逐步深入的讨论，并分别对常微分方程的初值问题和边值问题的数值求解计算给出了各自的方法。主要对常微分方程的初值和边值问题，将对其性质进行讨论，给出合理的数值解法且结合例子进行数值求解计算，并对各种方法进行了比较和分析。
关键词：常微分方程、初值问题、边值问题、数值解
Abstract
Ordinary differential equation is the powerful tool to study many natural science and technical issues, which has important practical value; thus it has an important practical value in mechanics, astronomy, physics, chemistry and biology in many issues. Because of a large number of phenomena which a large number of phenomena and the process obey can often be written in the form of ordinary differential equation, the equations themselves are the corresponding quantitative of the objective laws. The initial value problem and boundary value problem of ordinary differential equation is the one of basic calculations of ordinary differential equation, it runs through ordinary differential equation from beginning to end. The most of production problems and practical problems are the initial value problem and boundary value problem, there is not systematically in the materials, this article aims to classification summary with ordinary differential equation in the initial value problem and boundary value problem of the many complicated issues, to reach of initial value problem and boundary value problem with more detailed explore and summary. The following main issues are the solving calculation about initial value problem and boundary value problem of ordinary differential equation, from its property, carrying on going deep into gradually of discussion, and giving their methods of the numerical solution about the initial value problem and boundary value problem of ordinary differential equation. We will solve the initial value problem and boundary value problem of ordinary differential equation, discuss the property of the boundary value problem, provide a reasonable numerical solution method for calculating the numerical solution，and give kinds of the methods comparison and analysis.
Key words: ordinary differential equation, initial value problem, boundary value problem, numerical solution
目录
前言 1
第一章 常微分方程初值问题的描述 3
1.1 基本概念及定理 3
1.2 解对初值条件的连续依赖性和连续可微性 8
第二章 常微分方程边值问题描述 12
2.1 基本概念、定理及性质 12
第三章 常微分方程初值问题的数值方法求解 19
3.1 初值问题的数值解法 19
3.2 边值问题的数值解法 35
第四章 数值方法的收敛性分析及比较 42
4.1 数值方法的收敛性分析 42
4.2 数值方法的分析比较 43
结 论 45
谢 辞 46
参考文献 47
附 录 47
附录1 48
附录2 51
附录3 53
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论文题目：
微分方程的初边值问题(程序代码,PPT) 
