About
My name is Dmytro Sytnyk I am a researcher at the department of Computational Mathematics Institute of mathematics, National Academy of Sciences Ukraine. My scientific interests include numerical analysis, abstract theory of differential equations and their application to machine learning, in particular, to the development of new type of more efficient kernel methods and time-series forecasting algorithms. I am also interested in several adjacent topics ranging from linear algebra and theory of algorithms to parallel programming, scientific computing and simulation as well as modern software/hardware infrastructures, code optimization, etc.
Recent contributions:
- New criteria and sufficient conditions for the existence and uniqueness of solution to the nonlocal-in-time evolutionary problem for abstract first-order differential equation have been found. Based on these new conditions we developed a set of numerical tests to check the solvability of the given problem for arbitrary initial data from nonlocal condition.
- Using the technique proposed by I. Gavrilyuk and V. Makarov we developed a new exponentially convergent numerical method for the nonlocal-in-time evolutionary problem where the nonlocal condition is given in the form of linear combination of solution at different times.
- We explicitly determine elipticity conditions for several common 3, 4, 6, 8 bands effective mass Hamiltonians in terms of material parameter variables. It has been discovered that these multiband Hamiltonians, widely used in solid-state physic to determine a band structure of material, are non-elliptic for the majority of semiconductor material parameters.