一维逆热传导问题的一种数值解法 Alternative Title A Numerical Method For the Inverse Heat Conduction Problem 朱喜娜 Thesis Advisor 魏婷 2009-05-21 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 逆热传导问题 不适定问题 边界积分方程方法 Tikhonov正则化 GCV方法 Abstract 本文主要讨论了一个一维逆热传导问题，全文分为四个部分。 在论文的第一章，我们先简单介绍不适定问题的概念和一般的正则化理论，然后介绍了一些关于热传导问题的基本知识。 本文的第二章我们介绍了逆热传导问题背景以及目前的研究进展，还给出逆热传导问题的数学模型，包括它的正问题和反问题，并且分析反问题不适定性和解的唯一性。 在第三章中针对本问题引入边界积分方程方法，并且结合Tikhonov正则化方法给出了问题稳定解的一种求法，其中正则化参数是用\ GCV 方法求得的。 在第四章中是数值算例。 在最后一章，我们简单给出全文的结论。 Other Abstract In this paper, we consider a numerical method for the inverse heat conduction problem in one dimension.This paper is divided into four chapters. In chapter 1,we introduce the definition of the ill-posed problem and the general regularization theory,then we introduce some basic theory of the heat conduction problem. In chapter 2,we describe the background and development of the inverse heat conduction problem.Also we give the mathematical model of the inverse heat conduction problem,including its direct problem and inverse problem.We analyze the ill-posedness and uniqueness of the inverse problem. In chapter 3,we solve the problem using the method of boundary integral equation accompanied with Tikhonov regularization.And the regularization parameter is chosen by GCV function. In chapter 4,the numerical examples show that our propose numerical methods are effective. Finally, a conclusion is given in Chapter 5. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/224433 Collection 数学与统计学院 Recommended CitationGB/T 7714 朱喜娜. 一维逆热传导问题的一种数值解法[D]. 兰州. 兰州大学,2009.
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