Nonlinear Dynamics : міжнародна конференція
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/24521
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Документ Modeling of Nonlinear Environment with the Help of Families of the Atomic Functions(NTU "KhPI", 2016) Lisina, O. Yu.The procedure of constructing families of the atomic radial basis functions, which are recommended to be used to account for the heterogeneity of the environment in the simulation ofphysical processes is been considered. The solution of corresponding boundary problems are performed by meshless scheme, and the atomic functions are selected which satisfy the requirements. The families of infinitely differentiable compactly supported functions that are solutions of functional differential equations of special type had been considered. Expansion of classes of the atomic functions of several variables and expanding their properties considered is constructing a family of atomic radial basis functions of three independent variables on the example of the special type functionally-differentional equations. It should be noted that the support region is dependent on the compression ratio and can be specified in processes of construction solutions to provide the corresponding properties of the desired functions.Документ Atomic Functions: the History of the Formation, Development and Practical Application(NTU "KhPI", 2016) Kolodyazhny, V. M.Atomic functions are infinitely differentiable compactly supported solutions of functional differential equations of a special type. After the first successful building of the functions performed by VL Rvachev and VA Rvachev in the 70s of the previous century, different classes of the atomic functions of one and several variables were studied, which have found application in the solution of various problems of mathematical analysis and mathematical modeling of practical problems. Generalization of atomic functions to the case of several variables associated with the expansion of their possible application to solving boundary value problems in partial derivatives had been considered, in particular, and the development of new methods for the numerical solution of such tasks. Mathematical tools based on atomic functions of several variables have the necessary properties of universality and locality, to be requested in the practice of numerical solutions of boundary value problems. The study of functional differential equations, which are used for their formation other differential operators, fo rexample, Laplace, Helmholtz, biharmonic operators et al., leads to the construction of the special form of atomic functions. The atomic functions form the classes radial basis functions that allow you to develop on their basis meshless scheme of solving boundary value problems. In comparison with the known radial basis functions atomic radial basis functions have advantages, namely, are infinitely smooth, satisfy the functional-differential equation, effectively computable, have explicit formulas for the calculation of the Fourier transform.Документ R-Functions and WA-Systems of Functions in Modern Information Technologies(NTU "KhPI", 2016) Kravchenko, Victor F.; Kravchenko, Oleg V.; Konovalov, Yaroslav Yu.; Pustovoit, Vladislav I.; Churikov, Dmitry V.The review report consists of five parts. It describes the main physical applications of atomic, WA-systems and R-functions.