Application Of Total Variation-Based Regularization To The Inverse Problem Of A Kind Of Heat Equation

The aim of this thesis is to study how to gain stable numerical solution of a kind of heat equation. This inverse problem is a tipical ill-posed problem. To get its stable solution, Total Variation-Based Regularization is used. The method extends the solution space to the space of bounded variation functions instead of the space of continuous functions. Fixed-point iteration is used to solve the difficulty raised from nolinear of Euler equation and its glob;i.] convergence is prooved. Especially, in this thesis, the author makes an effort to give the method to choice the parameter a in Total Viriation-Based Regularization.The numerical experiment under the invironrnent of Matlab is also made to show the merits and to compare with the well-known Tikhonov Regularization. Thoeretical analysis and numerical test indicate that the new method and algorithoms possess the advantages of high-efficiency, good numerical stability, global convergence and so on.