Theoretical Estimation Of Two Regularization Methods For Solving Time-inverse Heat Conduction Problem

This paper deals with the problem of the time-inverse heat conduction problem,which is used to retrieve temperature from the temperature distribution at the final value.This problem is a serious ill-posed problem,although its solution exists but discontinuously depends on the data.It is very inconvenient for numerical com-putation,so a simple and convenient new quasi-reversibility regularization method and fractional Tikhonov regularization method is proposed to restore the continu-ous dependence of the solution on the data.In this paper,the quasi-reversibility regularization method is presented as long as the solution exists in the third deriva-tive,and the posterior parameter selection under the deviation principle is given.The regularization solution is obtained according to this method.Meanwhile,the convergence of errors between the approximate solution and the exact solution for the ill-posed problem is estimated,and the priori regularization parameter selection rules of the method are given.A numerical example is shown to demonstrate the effectiveness of the proposed method.