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Information × Registration Number 0223U001605, 0122U002026 , R & D reports Title Computational algorithms and optimization for artificial intelligence, medicine and defense popup.stage_title Head Liashko Serhii I., Доктор фізико-математичних наук Registration Date 31-01-2023 Organization Taras Shevchenko National University of Kyiv popup.description2 Research object: algorithms for solving direct and inverse problems, methods for finding transition points in time series, computational algorithms for variational inequalities, averaged problems, interpolation spline. The purpose of the work: to develop improved algorithms for solving direct problems of substance transfer in a porous medium; develop new non-parametric methods for finding transition points in time series; develop and research new adaptive algorithms for variational inequalities and game problems; develop new averaging methods for variational multiscale inequalities and equations; to develop and substantiate new piecewise polynomial approximation of discrete data sets, to analyze the possibilities of its application for applied problems, including the problem of data processing of trajectory measurements. Research method: computational experiment, mathematical modeling. An algorithm was developed, which is an analogue of the Ealorkin method for the initial-boundary problem that describes the transfer of substances in a porous medium. A method of numerical solution of the given initial-boundary value problem is constructed and theorems about its convergence to the solution are proved. A non-parametric method for detecting the transition point in multidimensional time series using tolerant ellipsoids has been developed. Numerical experiments demonstrated high accuracy and stability of the proposed algorithm in a wide range of distributions. New iterative algorithms for solving variational inequalities in uniformly convex Banach spaces have been studied. Initial boundary value problems for non-stationary filtration equations in periodic porous media formed by a large number of "blocks" with low permeability separated by a connecting system of "faults" with high permeability are considered. Averaged problems whose solutions determine the approximate asymptotics of the solutions of such problems are given.  Product Description popup.authors Veklych Olena A. Kliushyn Dmytro A. Sirenko Igor P. Sandrakov Gennadij V. Semenov Volodymyr V. Stelya Оleg B. popup.nrat_date 2023-01-31 Close