My recent research focuses on stochastic differential equations (SDEs), numerical methods for SDEs and applications in finance.
Key Scientific Results:
A spatial two-dimensional model of bottom material transport has been developed and investigated. The model allows predicting of bottom topography dynamics due to water and solid particles motion and accounts for soil porosity, critical shear stress for sediment motion, turbulent exchange, dynamically changing bottom geometry, wind-driven currents, and bottom friction. Achieved improved accuracy in spatial distribution estimates of pollutant concentrations and their impact zones [Sukhinov A.I. et al. Numerical Simulation of Dumping Consequences During Dredging in Coastal Marine Systems // Mathematical Physics and Computer Simulation 26:3, P. 37-55 (2023). DOI 10.15688/mpcm.jvolsu.2023.3.4 (in Russ.); Sukhinov A.I. et al. Modelling of suspended particles motion in channel // Journal of Physics: Conference Series 1479:1, P. 012082 (2020). DOI: 10.1088/1742-6596/1479/1/012082].
A finite difference scheme based on a linear combination of Upwind Leapfrog and Standard Leapfrog schemes for bottom material and suspended particle transport under high-intensity unidirectional flow is constructed. The scheme demonstrates superior accuracy for grid Péclet numbers between 2 and 20 [Sukhinov A.I. et al. Studying the Accuracy and Applicability of the Finite Difference Scheme for Solving the Diffusion-Convection Problem at Large Grid Péclet Numbers // Journal of Applied Mechanics and Technical Physics 62:7, P. 1255-1266 (2021). DOI 10.1134/S002189442107018X; Sukhinov A.I. et al. Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems // Mathematics 10:19, P. 3564 (2022). DOI: 10.3390/math10193564].
A 3D hydrodynamics model for shallow water bodies is constructed and investigated using B.N. Chetverushkin regularizers in the continuity equation [Sukhinov, A.I., Chistyakov, A.E., Kuznetsova, I.Y. et al. Regularized Difference Scheme for Solving Hydrodynamic Problems // Mathematical Models and Computer Simulations 14:5, P. 745-754 (2022). DOI: 10.1134/S2070048222050155; Chistyakov A.E., Nikitina A.V., Kuznetsova I.Y. et al. Investigation of the Approximation Error of the Difference Scheme for the Mathematical Model of Hydrodynamics // Lobachevskii J. Math. Vol. 44. P. 1839-1846(2023). DOI: 10.1134/S1995080223050128].
A software package for simulating dynamic changes in the bathymetry of shallow water bodies, applicable to forecasting scenarios of bottom geometry evolution is developed. [Sukhinov A.I. et al. Mathematical Model of Process of Sedimentation of Multicomponent Suspension on the Bottom and Changes in the Composition of Bottom Materials // Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 60, P. 73-89 (2022). DOI: 10.35634/2226-3594-2022-60-05].
Predictive modeling of aquatic pollution dispersion, including microplastic particles, using scenario-based approaches integrating hydrodynamics and biological kinetics models [Sukhinov A.I. et al. Analytical and Numerical Study of the Problem of the Plankton Population Dynamics in the Presence of Microplastics // Mathematical Models and Computer Simulations 16, P. 717-729 (2024). DOI: 10.1134/S2070048224700352]
Publications:
Kuznetsova I.Yu. has 62 scientific papers, including 5 articles in journals included in the Russian Science Citation Index (RSCI), 23 articles in journals from the current list of the Higher Attestation Commission (VAK) of Russia, and 22 articles in Scopus and Web of Science databases, also has 4 certificates of state registration of computer programs. Hirsch Index: 6 (RSCI), 3 (Scopus).
Awards:
Letter of Appreciation from the Head of the Administration of Taganrog (Decree No. 86-n, September 25, 2018).
Letter of Appreciation from the Governor of Rostov Region (Order No. 98, April 21, 2022).
