Registration Number
0214U003520,
0112U001284
, R & D reports
Title
Methods of research of the nonlinear dynamic systems, optimization problems, analysis of data based on Kohonen's maps
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Head
Prytula M.,
Registration Date
05-02-2014
Organization
Ivan Franko National University of Lviv
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The purpose of work: development of effective methods of research of the linear and nonlinear dynamic systems. Development of objective methods of analysis of data development of the effective mathematical and programmatic computer system data analysis software and environment of design of processes of navigation of intellectual agents. Construction of new algorithms which enable more effectively, in sense of amount of calculations, to get the results of solving of nonlinear functional equation and task of extremum. The organization of a research was carried out in next directions: Examined coefficients of Burgers type dynamical system, and found values of that coefficients when system possess an infinite hierarchy of invariant laws and has a pair of implectic operators. Using modified tanh-method have been got exact soliton solutions of considered system. Finite element schema with piecewise power basis functions for singularly perturbed boundary value problem with advection - diffusion equation has been suggested. Properties of these functions have been discussed. Optimal value of stabilization parameter has been found. The modification of the method of Lie algebraic approximations has been proposed in this work in the aim of solving one dimensional boundary value problem with inhomogeneous boundary value conditions. Scheme of the constructing the corresponding finite dimensional representation of differential operator has been investigated. The system of linear algebraic equations for direct solving the boundary value problem with inhomogeneous boundary value conditions has been obtained. Numerical investigations have been conducted via model problems. The task of construction of software is considered for the design of conduct of intellectual agents in a virtual environment. The analysis of existent decisions is conducted, outlined their advantages and failings. The basic requirements are formulated to the systems of such a type. The developed software which will realize the proposed requirements high-quality is considered. Description of the got system, and also grounded its efficiency and competitiveness, is resulted. The article deals with three-step iterative methods for solving many variables unconstrained minimization problems. The theoretical research method, set the third order of convergence. An accelerated Newton's method and difference methods for calculating a periodic responce in the nonlinear dynamical systems are applied. A clear algorithm for solving the problem is formulated.
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Бартіш Михайло Ярославович
Кіндибалюк Аркадій Анатолійович
Николайчук Леся Василівна
Огородник Наталя Пилипівна
Притула Микола Миколайович
Шахно Степан Михайлович
Щербина Юрій Миколайович
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2020-04-02
