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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| Published in: | Applied mathematics and computation Vol. 185; no. 1; pp. 564 - 573 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Inc
01.02.2007
Elsevier |
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Shi, Rui Qian, Zhi Fu, Chu-Li |
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| Cites_doi | 10.1016/j.ijheatmasstransfer.2003.12.019 10.1006/jcph.1995.1028 10.1007/s002110050073 10.1007/BF00282277 10.1016/S0096-3003(98)10010-3 10.1088/0266-5611/3/2/009 10.1080/10407790260233538 10.1007/BF00276168 10.1080/174159798088027679 10.1007/BF01594969 10.1016/S0017-9310(00)00235-0 10.1016/S0096-3003(02)00069-3 |
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| Keywords | 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 |
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| Snippet | 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... |
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| SubjectTerms | 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 |
| Title | A modified method for a backward heat conduction problem |
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