A comparison of some inverse methods for estimating the initial condition of the heat equation
Two explicit methods for the solution of an inverse heat conduction problem are analyzed. The authors confront them with the least-squares method, using for the solution of the associated direct problem a classical finite difference method and a method based on an integral formulation. Finally, the Tikhonov regularization connected with the least-squares criterion is examined. It is shown that the explicit approaches to this inverse heat conduction problem will present disastrous results unless some kind of regularization is used.
scientific article; zbMATH DE number 1331043