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摘要本文对于Adomian分解方法的最初建立思想以及后人对于该分解方法的修正作了简单的介绍，并给出了Adomian多项式的几个具体例子以及用Matlab求得Adomian多项式分解的结果。
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本文主要内容分为四部分。第一部分为绪论，简单叙述了Adomian分解方法的历史背景以及发展过程，归纳并总结了国内外学者对于Adomian分解方法的一些研究成果与应用。
接着，介绍了微分方程的幂级数方法。第三章详细介绍了Adomian分解方法以及后人对于此方法的一些修正和具体方法的应用过程，针对这种方法，本章也举了几个例子来说明。第四章针对前面提出的方法，用Matlab编程，将Adomian多项式的分解用程序实现。最后，对本文作了总结。38615
毕业论文关键词：Adomian分解方法，幂级数方法，微分方程，Adomian多项式
Computation and application of Adomian polynomials
Abstract
In this paper, we make a simple introduction to the original established thought of Adomian decomposition method and the revision of this method. Then we give some concrete examples about the Adomian polynomials and use MATLAB to obtain the results of Adomian polynomials decomposition.
This paper is pided into four chapters. The first chapter is the introduction, we make a brief description about the historical background and development process of the Adomian decomposition method, and summarize some foreign scholars’ research results and application of this method.
Then, the power series method of differential equation is introduced. After that, we make a detailed introduction about the Adomian decomposition method and the application of it. And as for this method, we give a few examples. In the fourth chapter, the application of Adomian polynomials is realized by MATLAB programming. Finally, the summary of this paper is made.
Key words: Adomian decomposition method, the power series method, differential equation, Adomian polynomials
目录
1.绪论 1
1.1Adomian分解方法的出现与发展 1
1.2Adomian分解方法的研究现状与应用 2
1.3 本文的研究目的和主要内容 2
2.预备知识 3
2.1 微分方程的幂级数方法 3
3.Adomian分解方法及Adomian多项式求解 7
3.1.逆算符方法简介 7
3.2 Adomian多项式算法 8
3.3 Adomian多项式的新算法 10
4.Adomian 多项式的Matlab实现 14
4.1 流程 15
4.2 用Matlab计算Adomian多项式的分解 15
4.3具体例子 17
5.Adomian分解法的应用 18
6.总结 19
7.致谢 20
8.参考文献 21
Contents
1.Introduction 1
1.1 The emergence and development of Adomian decomposition 1
1.2 The present situation and application of Adomian decomposition 2
1.3 The main purpose of this paper 2
2. Preparatory knowledge 3
The power series method of differential equation 3
3. Adomian decomposition method and the solution of Adomian polynomial 7
3.1 Introduction of inverse operator method 7
3.2 Calculation of Adomian polynomials 8
3.3 New algorithm of Adomian polynomials 10
4. the solution of Adomian polynomial with MATLAB 14
4.1 Calculation process 15
4.2 The decomposition of Adomian polynomials by Matlab 15
4.3 Examples 17
5. The application of Adomian decompositon 18