Inverse problem of time-dependent heat sources numerical reconstruction

Liu Yang, Mehdi Dehghan, Jian-Ning Yu and Guan-Wei Luo

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 8, 1656-1672

Abstract: This work studies the inverse problem of reconstructing a time-dependent heat source in the heat conduction equation using the temperature measurement specified at an internal point. Problems of this type have important applications in several fields of applied science. By the Green’s function method, the inverse problem is reduced to an operator equation of the first kind which is known to be ill-posed. The uniqueness of the solution for the inverse problem is obtained by the contraction mapping principle. A numerical algorithm on the basis of the Landweber iteration is designed to deal with the operator equation and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown heat source is recovered very well.

Keywords: Inverse problem; Heat source; Green function; Landweber iteration; Numerical results (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:8:p:1656-1672

DOI: 10.1016/j.matcom.2011.01.001

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