Numerical method for solving some inverse heat conduction problems with unknown initial conditions

The article deals with some inverse Cauchy problems for parabolic equations with unknown initial conditions. The principal possibility of construction the numerical solution of these problems in this domain is showed. The computational scheme is proposed which allows to construct the numerical solution of the inverse problem both on the whole domain and on the boundary under unknown initial conditions. To evaluate the efficiency of the proposed method the computational experiment was carried out. The results of the experiments show the sufficient stability of numerical solutions and the advantages of the proposed method.