Abstract
In this paper we investigate the numerical solution of the one-dimensional, time dependent heat conduction problem in which boundary conditions are specified at two space locations and the temperature distribution at a particular time, say T , is given. The temperature distribution and the heat flux for all time, t < T , are now required to be determined. This problem is an example of an inverse heat conduction problem and it is a well known improperly posed problem. In order to solve this problem the minimal energy technique, in conjunction with the Boundary Element Method, has been employed. In order to save computer storage, a time marching scheme is developed. The results show that the numerical solutions using the present technique are stable and accurate when compared to problems for which analytical solutions are known.
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