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Information × Registration Number 0216U007339, 0111U008971 , R & D reports Title Research of some classes of boundary problems of differential equations, their approximations and methods of processing of images popup.stage_title Head Vituk Aleksand Nikanorovich, Registration Date 27-07-2016 Organization Odessa I.I. Mechnikov National University popup.description2 Research report: 30, 1 table, 33 sources... Objects of research: problems of solid mechanics; equation with fractional derivatives; large sparse systems of linear equations; the problem of data visualization. Objective: To obtain new knowledge in the field of boundary value problems of solid mechanics, equations with fractional derivatives, methods for solving large systems with sparse matrices; development of image approximation methods. Research Methods: The methods of mathematical analysis, the theory of functions and differential equations; method of discontinuous solutions of problems of mechanics of destruction and detection of stress concentration at flaws; Krylov subspace iterative methods; Integrated image analysis methods and processing changes. An exact solution of the axisymmetric mixed problem of elasticity theory for the disadvantaged on the lateral surface of a cone with a ball attached segment is built. The problem of stress state inseparable strip plate, weakened fracture is solved. Proposed the method of calculation of continuous laminar structures with defects such as cracks or hard switching method based on three points. The existence and uniqueness of solutions of the Darboux problem for a differential equation with the regularized mixed derivatives of fractional order is proved. The existence of a generalized incomplete Cholesky decomposition of a saddle matrix is proved. Proposed the algorithm of temporal interpolation image sequence on the basis of generalized series Uayttaker Kotelnikova-Shannon. The results can be used by academic institutions for the implementation of the learning process and the continuation of research in the following areas: boundary value problems for differential equations with fractional derivatives; the construction of highly efficient methods for solving problems of mechanics of destruction and detection of stress concentration at flaws; methods for solving large linear systems with sparse matrices. PLATES, defect such as cracks, fractional derivatives, generalized decomposition, temporal interpolation image sequence. Product Description popup.authors Вербіцький Віктор Васильович Мороз Володимир Володимирович Реут Віктор Всеволодолвич Таірова Марія Сергіївна popup.nrat_date 2020-04-02 Close