On Three Spectral Regularization Methods for a Backward Heat Conduction Problem
نویسندگان
چکیده
We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.
منابع مشابه
A regularization method for solving a nonlinear backward inverse heat conduction problem using discrete mollification method
The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...
متن کاملBoundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method
In this paper, we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain. This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve. To this end, the boundary integral equation method is used. Since the resulting system of linea...
متن کاملCentral Difference Regularization Method for Solving a Backward Heat Conduction Problem
Non-standard backward heat conduction problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In this paper, we proposed a regularization strategy-central difference method to analysis the stability of the problem. Meanwhile, we investigate the function of the regularization parameter, two numerical implementations are described. Numerical exa...
متن کاملThe Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems
The Lie-Group Shooting Method for Quasi-Boundary Regularization of Backward Heat Conduction Problems Chih-Wen Chang1, Chein-Shan Liu2 and Jiang-Ren Chang1 Summary By using a quasi-boundary regularization we can formulate a two-point boundary value problem of the backward heat conduction equation. The ill-posed problem is analyzed by using the semi-discretization numerical schemes. Then, the res...
متن کاملTwo numerical methods for solving a backward heat conduction problem
We introduce a central difference method and a quasi-reversibility method for solving a backward heat conduction problem (BHCP) numerically. For these two numerical methods, we give the stability analysis. Meanwhile, we investigate the roles of regularization parameters in these two methods. Numerical results show that our algorithm is effective. 2005 Elsevier Inc. All rights reserved.
متن کامل