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Information × Registration Number 0221U104036, 0116U003063 , R & D reports Title Exponentially convergent methods for spectral problems, problems for quasilinear equations with unbounded operator coefficients and rational approximation of multivariate functions popup.stage_title Head Makarov Volodymyr L., Доктор фізико-математичних наук Registration Date 01-03-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2  The scientific report is devoted to the development and substantiation of numerical methods for solving problems described by differential, integral and functional equations; as well as some questions of approximation of functions of one and many variables and interpolation of functions and operators. An exponentially convergent method for numerical solution of problems for a first-order differential equation with an unlimited operator coefficient in Banach space and various nonlocal conditions is constructed. The time-inverse problem for a first-order differential equation with an unbounded operator coefficient in Banach space is investigated. An exponentially convergent numerical method for approximatіng its solution is constructed and substantiated. A wide range of issues of modern theory of interpolation and approximation is considered. In particular, an interpolation integral chain fraction of the Tile type is constructed, and a generalized interpolation fraction of the Tile type is proposed for the approximation of nonlinear functionals. The criteria for the solvability of the problem of interpolation of a functional by an integral chain C-fraction are found, when its values ​​on a continuum set of nodes are known. Pade-type approximants for some classes of functions of several variables are constructed and investigated by extending the method of generalized instantaneous images of V.K. Dzyadyk to a multidimensional case. A functional-discrete (FD) method for finding exact solutions of one-dimensional spectral problems for the Schrödinger operator with polynomial potential is proposed, and a recurrent algorithm for finding partial solutions of partial solutions of resonant equations of the first and differential equations of the first and different equations of the first is constructed and substantiated. Product Description popup.authors Vasylyk Vitalii B. Veselovska Hanna M. Holub Anatolii P. Komaaschenko Nina O. Pozharskii O. A. Sytnyk Dmytro O. Snihur Tetyana O. Chernetska Liliya O. popup.nrat_date 2021-03-01 Close