Heat Conduction Problems Numerical Methods Based On The Inverse Of The Difference Method

The aim of this paper is to present an inversion scheme for 2-D backward heat problem of determining the initial temperature distribution from its final measurement given at some time T > 0. There are two characters of this problem. First, it does not exist solution on any given function f(x). Second, the data of its initial temperature does not have continuous dependence on the temperature field of t = T. That is to say the problem is ill-posed. Therefore, we need to discuss the numerical method for the stability of approximate solution. This paper is based on regularizing method and SOR iteration to solve this problem.The paper is organized as follows. In chapter 1, we introduce the basic knowledge of the inverse problem. In chapter 2. we give the related property and regularizing methods. In chapter 3. we give the mathematical model for direct heat problem, and construct a new computational algorithm which based on the difference scheme for the spatial discretization, and the fourth-order Runge-Kutta scheme for the temporal discretization, then the error analysis is also given. In chapter 4. we introduce the mathematical model of 2-D inverse heat conduction problem, after regularizing the inverse problem , we use the SOR iteration to solve this equation, the numerical results of our regularized inversion are also presented.