A modified method for a backward heat conduction problem

We consider a backward heat conduction problem in a strip, where data is given at the final time t = T( T > 0) and a solution for 0 ⩽ t < T is sought. The problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In order to numerically solve t...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 185; no. 1; pp. 564 - 573
Main Authors: Qian, Zhi, Fu, Chu-Li, Shi, Rui
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.02.2007
Elsevier
Subjects:
Backward heat conduction
Exact sciences and technology
Ill-posedness
Mathematical analysis
Mathematics
Modified method
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Regularization
Sciences and techniques of general use
Regularization
Modified method
Ill-posedness
Backward heat conduction
s: Backward heat conduction
Approximation
Error estimation
Numerical linear algebra
Regularization method
Numerical analysis
Third order equation
Applied mathematics
Numerical solution
Ill posed problem
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:We consider a backward heat conduction problem in a strip, where data is given at the final time t = T( T > 0) and a solution for 0 ⩽ t < T is sought. The problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In order to numerically solve the problem, we study a modification of the equation, where a third-order mixed derivative term is added. Error estimates for this problem are given, which show that the modified problem is stable and its solution is an approximation of the backward heat conduction problem. Some numerical tests illustrate that the proposed method is feasible and effective.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2006.07.055