Identification of parameters in one-dimensional IHCP

We present a new numerical method based on discrete mollification for identification of parameters in one-dimensional inverse heat conduction problems (IHCP). With the approximate noisy data functions (initial temperature on the boundary t = 0, 0 less than or equal to x less than or equal to 1, temperature and space derivative of temperature on the boundary x = 0, 0 less than or equal to t less than or equal to 1) measured at a discrete set of points, the diffusivity coefficient, the heat flux, and the temperature functions are approximately recovered in the unit square of the (x, t) plane. In contrast to other related results, the method does not require any information on the amount and/or characteristics of the noise in the data and the mollification parameters are chosen automatically. Another important feature of the algorithm is that it allows for the recovery of much more general diffusivity parameters, including discontinuous coefficients. Error bounds and numerical examples are provided.