We consider a non-standard inverse heat conduction problem in a bounded domain which appears in some applied subjects. We want to know the surface temperature in a body from a measured temperature history at a fixed location inside the body. This is an exponentially ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we introduce the two new classes of quasi-type methods and iteration methods to solve the problem and prove that our methods are stable under both a priori and a posteriori parameter choice rules. An appropriate selection of a parameter in the scheme will get a satisfactory approximate solution. Furthermore, if we use the discrepancy principle we can avoid the selection of the a priori bound.
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