Improvement of the accuracy of solution of tasks for the account of the construction of boundary conditions

The problems of stability of the solution of inverse problems with respect to the exact setting of boundary conditions are considered. In practical applications, as a rule, the theoretical form of the functional dependence of the boundary conditions is a form that is not defined or not known, and there are also random measurement errors. Studies have shown that this leads to a significant reduction in the accuracy of solving the inverse problem. In order to increase the accuracy of solving inverse problems, it was proposed to refine the functional form of the boundary conditions by recognizing the form of the mathematical model of dependence with the subsequent approximation by this function of the behavior of a physical quantity at the boundary. Dependency recovery was performed using dependency recognition methods based on structural difference schemes and inverse mapping recognition. Model examples of implementation in the presence of additive random measurement errors and an unknown type of dependence of the boundary conditions are given.