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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Vydané v:	Applied mathematics and computation Ročník 185; číslo 1; s. 564 - 573
Hlavní autori:	Qian, Zhi, Fu, Chu-Li, Shi, Rui
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY Elsevier Inc 01.02.2007 Elsevier
Predmet:	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
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Popis
Shrnutí:	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