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Information × Registration Number 0224U033536, (0124U002111) , R & D reports Title New approaches and methods of the theory of boundary value problems and their application to the study of mathematical models of complex processes of support and recovery of the national economy popup.stage_title Розробка нових підходів та методів теорії крайових задач Head Olga V. Nesmelova, Доктор фізико-математичних наук Registration Date 30-12-2024 Organization Institute of Applied Mathematics and Mechanics National Academy of Science of Ukraine popup.description1 The purpose of the research work is to develop new approaches and methods for studying the properties, obtaining the conditions of solvability, constructing effective schemes for finding solutions to linear and nonlinear boundary value problems for ordinary differential, differential-algebraic, integal-differential and elliptic equations with various boundary conditions and applying them to the analysis and prediction of complex processes arising in various sectors of economic activity and industry. popup.description2  The aim of Phase I of the project was developing new approaches and methods for studying properties, obtaining solvability conditions, and building efficient schemes for finding solutions to linear and nonlinear boundary value problems for ordinary differential, differential-algebraic, integro-differential, and elliptic equations with various boundary conditions. During 2024, the following main results were obtained: 1. Conditions for the solvability of a nonlinear boundary value problem unsolved with respect to the derivative were obtained. The application of the obtained iterative schemes is demonstrated on the example of a Rayleigh-type equation and an equation modelling the motion of a satellite. 2. The conditions for the solvability of a nonlinear boundary value problem for a system of integro-differential equations are obtained, and a convergent iteration process is constructed. It is established that the described mathematical model has a wide range of applications for forecasting and analysing economic processes. 3. For linear nonhomogeneous boundary value problems for systems of ordinary equations, under the condition of maximum generality of the boundary value operator, the Fredholm numbers and the index of boundary value problems are found, and the conditions of their solvability are obtained. 4. A new approach to the study of elliptic boundary value problems with coarse boundary data is developed, based on the interpolation of functional spaces of distributions generated by some elliptic operator defined in a bounded domain. Product Description popup.authors Bondar Ivanna A. Soldatov Vitalii O. Chepurukhina Iryna S. popup.nrat_date 2024-12-30 Close