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Information × Registration Number 0220U100672, 0119U100337 , R & D reports Title Mathematical modeling and optimization of dynamic systems for defense, ecology and medicine. popup.stage_title Head Lyashko Sergei Ivanovich, Registration Date 23-01-2020 Organization Taras Shevchenko National University of Kyiv popup.description2 Object of study: Algorithms for solving variational inequalities, multilevel variational problems and fast learning of neural networks. Processes described by stationary and non-stationary convection-diffusion-reaction equations, which contain a small parameter at a higher derivative. The trajectories of the movement of fledged and fledged projectiles in perturbed air. Parameters of ballistic models affecting projectile movement. Purpose of the project: The purpose of the project is to create and study efficient algorithms for variational inequalities, multilevel variational problems and rapid learning of neural networks; construction and justification of a monotonic conservative difference scheme for small-parameter convection-diffusion-reaction equations at a senior derivative; development of algorithms and computer implementation of models of external ballistics for flared shells and mines, taking into account the moments of inertia. Research method: Nurminski schemes and Feuer technique, Nester's fast gradient scheme, methods of a priori estimations in negative spaces, methods of averaging differential equations in partial derivatives, difference methods. The uniqueness of the generalized solution is proved, a priori estimates for negative spaces for functions satisfying the conditions of direct and conjugate problems are proved. The auxiliary integral operator and the Sylvester criterion were used for the proof. The conditions of existence of optimal control and the gradient of the quality criterion are given. Focused initial boundary value problems are constructed and substantiated, the solutions of which approach the solutions of the given boundary value problem, which simulates the processes of multiphase diffusion and filtration in porous media. Methods for solving variational inequalities with explicit character are proposed, that is, at the iterative step, only the values ​​of the operators are calculated and the design is allowed for a valid set. Product Description popup.authors Veklych Olena A. Hulianytskyi Leonid F. Kivva Tetyana S. Kyrychenko Ivan V. Кlyushyn Dmytro A. Lyashko Sergiy I. Potapenko Leonid I. Sirenko Igor P. Sandrakov Gennadij V. Semenov Volodymyr V. Stanislavska Svitlana V. Stelya Оleg B. Tereschenko Yaroslav V. Cherniy Dmytro I. popup.nrat_date 2020-04-02 Close