Valko N. Probabilistic models and methods barycentric averagings of boundary potentials

The dissertation is devoted to construction of models and methods barycentric averagings for problems of restoration of harmonious functions. In work new models barycentric averagings of boundary potentials are constructed. The new approach which, on the basis of the weighed averaging, unites various classical methods is offered. It promotes development of new, more effective algorithms of the weighed averaging. Conditions of convergence of the scheme barycentric averagings are received at the decision of problem Dirichlet for equations Laplace and Poisson in separate areas. Effective algorithms barycentric averagings of boundary potentials due to use of units of the raised convergence are developed. It has allowed to reduce quantity of calculations for reception of the approached decision of separate problems. It does a method barycentric averagings effective on cases when it is necessary to receive the approached decision of equations Laplace and Poisson in separate points of area by means of a smallamount enough simple calculations.