The major difficulty of the inverse problem lies in the fact that its solution does not depend continuously on the data and therefore is ill-posed.Based on Tikhonov's regularization method

a numerical procedure is provided for processing the input data in the inverse heat transfer problem

so that a uniform approximation is obtained both for the data function and its derivative.The effectiveness of the methods illustrated through simulated experiments using inexact data.The results demonstrate that the accuracy and stability of the inverse problem solution are significantly improved.The influence of the time step and the regularization parameter is also investigated.In addition

it is also shown that such a regularizing smooth procedure is obviously superior to the ordinary least square approximate method.