Method for solving some multidimensional inverse boundary value problems for parabolic PDEs without initial conditions

This paper proposes a new method for solution of some inverse boundary value problems with unknown initial conditions. The method is based on the use of finite-difference schemes and its application has regularized solutions both at the border and throughout the area under consideration with unknown initial conditions. The proposed method is the basis for the development of a numerical method for the solution of inverse boundary value problems with unknown initial conditions. The computational experiment was carry out in order to evaluate the effectiveness of the proposed method and obtaining experimental error estimates. During the experiment numerical solutions of problems with constant and variable coefficient within the whole domain and on its boundary were obtained. The experiment results are presented in the paper. These results indicate the sufficient stability and the efficiency of the proposed method solutions.