Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 267, pp. 114.
Stable algorithm for identifying a source in the heat equation
Lahcene Chorfi, Leila Alem
Abstract:
We consider an inverse problem for the heat equation
in the quarter plane
where one wants
to determine the temperature
from the measured data
.
This problem is severely illposed and has been
studied before. It is well known that the central difference
approximation in time has a regularization effect, but
the backward difference scheme is not well studied in
theory and in practice. In this paper, we revisit this method
to provide a stable algorithm. Assuming an a priori bound on
we derive a Holder type stability result.
We give some numerical examples to show the efficiency of the
proposed method. Finally, we compare our method to one based on
the central or forward differences.
Submitted June 27, 2015. Published October 16, 2015.
Math Subject Classifications: 35K05, 65M32, 65T50.
Key Words: Inverse problem; heat equation; fourier regularization;
finite difference.
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Lahcène Chorfi
Laboratoire de Mathématiques Appliquées
Université B. M. d'Annaba
B.P. 12, 23000 Annaba, Algérie
email: l_chorfi@hotmail.com


Leïla Alem
Laboratoire de Mathématiques Appliquées
Université B. M. d'Annaba
B.P. 12, 23000 Annaba, Algérie
email: alemleila@yahoo.fr

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