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Information × Registration Number 0223U004334, 0121U110612 , R & D reports Title Methods of high-performance computing for the study of mathematical models of complex dynamical systems popup.stage_title Head Makarov Volodymyr L., Доктор фізико-математичних наук Registration Date 13-10-2023 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2  MATHEMATICAL MODEL, EXPONENTIALLY CONVERGING METHOD, METHOD WITHOUT ACCURACY SATURATION, FRACTIONAL DIFFERENTIAL EQUATION, KELLY TRANSFORMATION, NUMERICAL DIFFERENTIATION, TIKHONOV REGULARIZATION METHOD, SMOOTHING OF THREE-DIMENSIONAL OBJECTS , PROBLEMS WITH A FREE BOUNDARY, LIQUID OSCILLATIONS IN TANKS. Object of research --- a problem for a fractional-differential equation, a problem of numerical differentiation, a problem of fluid fluctuations in tanks with a free surface, a problem of smoothing three-dimensional objects. The purpose of the work --- is the solution of actual problems related to the mathematical modeling of complex dynamic systems that describe the interaction of objects of different physical nature and arise during the development of modern technologies, as well as a series of complex topical problems of computational mathematics of high-performance computing. From a mathematical point of view, the objects of research are: nonlinear boundary value problems of a special type (including those with a free boundary), for which fundamentally new numerical approaches are proposed; algorithms for building solutions to mathematical physics problems in areas with a complex geometric shape; development and implementation of new data classification methods in the scheme of active machine learning using nonlinear methods of dimensionality reduction based on diffusion transformations and operator functions related to them, which are also planned to be used to restore the coefficients of mathematical models with a small amount of experimental data (the so-called problems " hidden physics"); development of the theory of complexity of incorrect problems and substantiation of optimal methods of solving unstable problems. The developed numerical methods should provide for the possibility of parallelizing calculations for their implementation on supercomputer systems and in distributed computing environments ("scientific clouds"). Research methods --- methods o Product Description popup.authors Vasylyk Vitalii Sytnyk Dmytro Solodkiy Serhii Timokha Oleksandr popup.nrat_date 2023-10-13 Close