A Numerical Method For The Inverse Heat Conduction Problem In One Dimension

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 review some basic results of the heat conduction problem.In Chapter 2,the background and development of the inverse heat conduction problem are described.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 the Tikhonov regularization.And the regularization parameter is chosen by GCV rule.In Chapter 4,the numerical examples show that our propose numerical methods are effective.Finally,a conclusion is given in Chapter 5.