Method for temperature measuring in the rod with heat source under uncertain initial temperature

In this contribution, the problem of linear heating a object with unknown initial temperature by external thermal point source is considered. The object has an internal heat source. External terminal source is located on part of the boundary and we made the indirect dynamic measurements on the same part of the boundary. We propose a method for calculating temperature inside the body. This method is based on the measurement results under condition when the initial temperature of the object cannot be measured. The computing scheme of the method is based on using finite-difference schemes and discrete regularization method. We prove the conditional stability of the method and estimate the temperature errors via accuracy of the boundary measurements. The theoretical error estimates and computational results confirm sufficient efficiency and reliability of the proposed computational scheme.