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This paper proposes a numerical method to deal with the one-dimensional inverse heat conduction problem (IHCP). The initial temperature, a condition on an accessible part of the boundary and an additional temperature measurements in time at an arbitrary location in the domain are known, and it is required to determine the temperature and the heat flux on the remaining part of the boundary. Due to the missing boundary condition, the solution of this problem does not depend continuously on thedoi:10.5899/2013/cna-00172 fatcat:ipuww3ilfba5dp2s4nnnlh2nle