• numerical methods of solving boundary value problems
• finite element method
• singularly perturbed diffusion-advection-reaction problems
• adaptive and stabilized schemes of the finite element method
• quantum computing
• optimization of algorithms
• construction of methods for solving singularly perturbed diffusion-advection-reaction problems based on a combination of classical and quantum algorithms

• Go (Golang) Programming (cs)
• Industrial (Computing) Practice (KIS)
• Production practice (cs, masters)

Articles:

Unpublished (work in progress):

• Drebotiy R. Convergence of the directional diffusion splitting method / R. Drebotiy, H. Shynkarenko // [preprint] arXiv:2411.12305 [math.NA] https://doi.org/10.48550/arXiv.2411.12305
• Drebotiy R. Directional diffusion splitting method for advection-diffusion-reaction model / R. Drebotiy, H. Shynkarenko // [preprint] arXiv:2411.11041 [math.NA] https://doi.org/10.48550/arXiv.2411.11041
• Drebotiy R. Quantum-assisted hλ-adaptive finite element method / R. Drebotiy, H. Shynkarenko // [preprint] arXiv:2411.12687 [math.NA] https://doi.org/10.48550/arXiv.2411.12687

In print:

• Drebotiy R. Modified heuristic criterion for parameter choice for one stabilization scheme of the finite element method / R. Drebotiy, H. Shynkarenko // Journal of Applied and Numerical Analysis. – Lviv, 2024

Published:

• Drebotiy R. Fully parallel algorithm for solution of advection-reaction Cauchy problem in one finite element regularization scheme / R. Drebotiy, V. Stelmashchuk, H. Shynkarenko // Manufacturing Processes. Actual Problems.– Politechnika Opolska.– Opole, 2023.– Vol. 1.– Pp. 35-44.
• Drebotiy R. Heuristic choice of the regularization parameter for optimal stabilization of the finite element approximations / R. Drebotiy, H. Shynkarenko // Mathematical Methods and Physicomechanical Fields. – Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine. – Lviv, 2023,  Vol. 66, No. 1-2, 206–221. – https://doi.org/10.15407/mmpmf2023.66.1-2.206-221
• Drebotiy R. Finite element analysis of Green-Lindsay thermopiezoelectricity time-dependent problem / R. Drebotiy, V. Stelmashchuk, H. Shynkarenko // Visnyk of the Lviv University. Series Appl.Math. and Informatics. – Lviv, 2023.–Issue 31.
• Drebotiy R. Regularized finite element method for singular perturbed convection-diffusion-reaction models with nonuniform sources / R. Drebotiy, H. Shynkarenko // Visnyk of the Lviv University. Series Appl.Math. and Informatics.– Lviv, 2021.– Issue 29.
• Drebotiy R. Elementwise decomposition of a posteriori error estimator based on reference solution for hp-adaptive finite element method / R. Drebotiy, H. Shynkarenko // Visnyk of the Lviv University. Series Appl.Math. and Informatics.– Lviv, 2018.– Issue 26.- Pp. 56-69
• Drebotiy R. On the application of the one hp-adaptive finite element strategy for nonsymmetric convection-diffusion-reaction problems / R. Drebotiy, H. Shynkarenko // Journal of Numerical and Applied Mathematics, ISSN: 0868-6912.– Kyiv, 2017.– Issue 3(126). Pp. 48-60.
• Drebotiy R. Symmetrization of diffusion-advection-reaction problem and hp-adaptive finite element approximations / R. Drebotiy, H. Shynkarenko // Visnyk of the Lviv University. Series Appl.Math. and Informatics.– Lviv, 2015.– Issue 23.– Pp. 55–72.
• Drebotiy R. hp-adaptive finite element method for 1D diffusion-convection-reaction boundary value problems / R. Drebotiy, H. Shynkarenko // Manufacturing Processes. Actual Problems.– Politechnika Opolska.– Opole, 2014.– Vol. 1.– Pp. 11–26.
• Drebotiy R. Comparison of error indicators and refinement criteria for hp-adaptation algorithm for finite element method / R. Drebotiy, H. Shynkarenko // Visnyk Odeskoho Natsionalnoho Universytetu. Matematyka i Mekhanika.– Odessa, 2014.– V.19, Is. 4(24).– Pp. 45–57.

Textbooks/tutorials:

• Drebotiy R. H., Stelmashchuk V. V. Programming in Go language : tutorial / Lviv : Ivan Franko National University of Lviv, 2024. – 64 p. – ISBN 978-617-10-0845-8. (in Ukrainian)

Educational and methodological materials:

• Methodical guidelines for completing master’s theses for students of the “master’s” qualification level, specialty 122 Computer science, educational program “Informatics” / Comp.: R. H. Drebotiy, V. V. Stelmashchuk – Lviv: Ivan Franko National University of Lviv, 2023. – 28 p. (in Ukrainian)

Conference materials:

• Drebotiy R. Diffusion splitting method for non-stationary diffusion-advection-reaction problems // 11th International Scientific Conference “Mathematical problems of mechanics of nonhomogeneous structures”. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, September 24-26, 2024 – Lviv, 2024. – P. 161–162.
• Drebotiy R. Application of certain hp-adaptive finite element strategy to nonsymmetric convection-diffusion-reaction problems / R. Drebotiy, H. Shynkarenko // Ukrainian Conference on Applied Mathematics (dedicated to the 100th birth anniversary of Professor Olexandr Kostovskiy). Ivan Franko National University of Lviv, September 28-30, 2017 – Lviv, 2017. – P. 45–46.
• Drebotiy R. On some properties of a posteriori error estimator based on reference solution for hp-adaptive finite element method // Сучасні проблеми прикладної математики та інформатики: Матер. доп. XХІV Всеукр. наук. конф. 26-28 вересня 2018 р., м. Львів. – Львів : Видавництво Тараса Сороки, 2018. – С. 54–55.
• Drebotiy R. A posteriori error estimator based on fundamental solution for 1D hp-adaptive FEM approximation [Електронний ресурс] / R. Drebotiy, H. Shynkarenko // Конференцiя молодих учених «Пiдстригачiвськi читання-2017», (Інститут прикладних проблем механіки і математики імені Я. С. Підстригача НАН України, 23-25 травня 2017). – Львiв, 2017. – Режим доступу: http://iapmm.lviv.ua/chyt2017/abstracts/Drebotiy.pdf
• Drebotiy R. Gaussian quadrature implementation for hp-adaptive finite element method / R. Drebotiy // Сучасні проблеми прикладної математики та інформатики: Матер. доп. XХІІ Всеукр. наук. конф. 5-7 жовтня 2016 р., м. Львів. – Львів : Видавничий центр ЛНУ, 2016. – С. 9–12.
• Drebotiy R. Symmetrization of diffusion-advection-reaction problem and hp-adaptive finite element approximations / R. Drebotiy // XIX Всеукраїнська (XIV Міжнародна) наукова студентська конференція з прикладної математики та інформатики (Львівський національний університет імені Івана Франка, 14-15 квітня 2016р.): Матерiали конференцiї. – Львiв : Видавничий центр ЛНУ, 2016. – C. 46–47.
• Drebotiy R. A posteriori error estimators for hp-adaptive finite element method / R. Drebotiy // Сучасні проблеми прикладної математики та інформатики: Матер. доп. XХІ Всеукр. наук. конф. 24-25 вересня 2015 р., м. Львів. – Львів : Видавничий центр ЛНУ, 2015. – С. 27–30.
• Drebotiy R. Symmetrization of diffusion-advection-reaction boundary value problem and its hp-finite element approximations / R. Drebotiy, H. Shynkarenko // VII Int. Conf. named by I. I. Lyashko “Computational and applied mathematics” (Taras Shevchenko National University of Kyiv, October 9-10, 2014): Short papers. – Kyiv, 2014. – P. 119–120.
• Drebotiy R. hp-adaptive finite element approximation for 1D boundary value problems [Електронний ресурс] / R. Drebotiy, H. Shynkarenko // Конференцiя молодих учених «Пiдстригачiвськi читання-2014», (Інститут прикладних проблем механіки і математики імені Я. С. Підстригача НАН України, 28-30 травня 2014). – Львiв, 2014. – Режим доступу: http://www.iapmm.lviv.ua/chyt2014/theses/Drebotiy.pdf
• Drebotiy R. hp-adaptive FEM for 1D boundary value problems / R. Drebotiy // Сучасні проблеми прикладної математики та інформатики: Матер. доп. XХ Всеукр. наук. конф. 7-9 квітня 2014 р., м. Львів. – Львів: Видавничий центр ЛНУ, 2014. – С. 13–14.
• Drebotiy R. Residual hp-adaptive FEM for 1D diffusion-convection-reaction boundary value problems / R. Drebotiy, H. Shynkarenko // VI Int. Conf. named by I. I. Lyashko “Computational and applied mathematics” (Taras Shevchenko National University of Kyiv, September 5-6, 2013): Short papers. – Kyiv, 2013. – P. 18–21.
• Drebotiy R. A posteriori error estimators and hp-adaptive FEM for 1D diffusion-convection-reaction boundary value problems / R. Drebotiy, H. Shynkarenko // V Int. Conf. named by I. I. Lyashko “Computational and applied mathematics” (Taras Shevchenko National University of Kyiv, September 10-11, 2012): Short papers. – Kyiv, 2012. – P. 17–17.
• Дреботій Р. Апроксимації h-адаптивного МСЕ для одновимірних крайових задач / Р. Дреботій, Ю. Ладанівський // XIV Всеукраїнська (IX Міжнародна) наукова студентська конференція з прикладної математики та інформатики (Львівський національний університет імені Івана Франка, 5-6 травня 2011 р.): Матерiали конференцiї. – Львiв : Видавничий центр ЛНУ, 2011. – C. 208–209.

Born in Lviv, Ukraine
EDUCATION AND SCIENTIFIC CAREER:
2019 – Obtained a degree of candidate of physical and mathematical scinces (PhD) for the dissertation “Construction and analysisof hp-adaptive finite element method for diffusion-convection-reaction problems”
2008 – 2013 – Faculty of Applied Mathematics and Informatics of Ivan Franko National University of Lviv
1998 – 2008 – Lviv school No 100
JOBS:
2022 – present – Associate Professor of Department of Information Systems of Ivan Franko National University of Lviv
2013 – 2022 – Assistant Lecturer of Department of Information Systems of Ivan Franko National University of Lviv

Textbooks/tutorials:

• Drebotiy R. H., Stelmashchuk V. V. Programming in Go language : tutorial / Lviv : Ivan Franko National University of Lviv, 2024. – 64 p. – ISBN 978-617-10-0845-8. (in Ukrainian)

Educational and methodological materials:

• Methodical guidelines for completing master’s theses for students of the “master’s” qualification level, specialty 122 Computer science, educational program “Informatics” / Comp.: R. H. Drebotiy, V. V. Stelmashchuk – Lviv: Ivan Franko National University of Lviv, 2023. – 28 p. (in Ukrainian)

1st semester
2nd semester