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Information × Registration Number 0217U001765, 0117U002829 , R & D reports Title Development of mathematical modelling methods and approximation theory for the solution of actual problems of modern natural science. popup.stage_title Head Makarov Volodymyr Leonidovych, Registration Date 18-05-2017 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Scientific report dedicated to the development and justification of numerical methods for solving problems described by differential, integral and functional equations in the nonclassical settings; and some questions on approximation of functions of one and many variables as well as interpolation functions and operators. Necessary and sufficient conditions for the existence of solution of nonlocal in time problem for the 1st order differential equations with unbounded operator coefficient and linear non-local multipoint condition are obtained. New sufficient conditions for the existence of solution of the mention problem that generalize the available literature counterparts are formulated. Authors developed and justified exponentially convergent numerical method for the solution of the said non-local problem. They also developed exponentially convergent method for differential equations with unbounded operator coefficient in Banach space with the condition in the final moment, which is based on the regularization using non-local conditions. The developed numerical methods are methods without saturation of accuracy. The report addressed a number of important extremal problems of the approximation theory in classes of single- and multi-varied functions. New order estimates for the best approximation by Fourier sums and other orthogonal trigonometric approximations of some classes of functions are found; Authors exactly calculated some constants from the Landau-Wiener --type inequalities for the coefficients of Taylor serries for bounded holomorphic functions of several variables; New analytical representations of polylogariphms are obtained; Authors derived the exact values of some important characteristics of Orlicz spaces; In addition to that the order of entropy numbers for the classes of Nikolsky-Besov of multivaried periodic functions are established; New multiple Haar-type basis is developed for the Lebesgue spaces; Exact (with respect to the order) estimates for the Kolmogorov diameters and entropy numbers for classes of Nikolsky-Besov -type with logarithmic smoothness are found. The problem of reducing the amount of information costs in the numerical solution of periodic elliptic integral equations were considered. To solve this problem authors proposed and justified a modification of completely discrete projection method in combination with the discretization level selection strategy. It is proved that this approach provides the best accuracy, among the family of subquadratic algorithms, for the target class of problems in Sobolev spaces. The application of Student's t test was used to statistically prove the differences between the averages of indicators of certain medical characteristics of patients in the groups "before treatment" and "after the 6th treatment" (i.e. after the completion of treatment). Product Description popup.authors Бакан Андрій Генадійович Василик Віталій Богданович Голуб Анатолій Петрович Конограй Андрій Федорович Макаров Володимир Леонідович Нестеренко Борис Борисович Новотарський Михайло Анатолійович Романюк Анатолій Сергійович Романюк Віктор Сергійович Романюк Наталія Миколаївна Савкіна Марта Юріївна Савчук Віктор Васильович Семенова Євгенія Вікторівна Сердюк Анатолій Сергійович Ситник Дмитро Олексійович Соколенко Ігор Володимирович Солодкий Сергій Григорович Стасюк Сергій Андрійович Шидліч Андрій Любомирович Янченко Сергій Якович popup.nrat_date 2020-04-02 Close