The results of scientific research are regularly reported at seminars, international and foreign conferences, and published in highly rated journals.
From January 10, 2022 to December 14, 2022, he worked as a leading programmer of the Laboratory of Electromagnetic Radiation of the Institute of Cosmophysical Research and Radio Wave Propagation of the Far East Branch of the Russian Academy of Sciences.
From December 15, 2022 to the present, he has been working as a research associate of the Laboratory of Electromagnetic Radiation of the Institute of Cosmophysical Research and Radio Wave Propagation of the Far East Branch of the Russian Academy of Sciences.
Executor of grants from RFFR, RSF, and the President of the Russian Federation.
Head of the RSF grant.
Main publications:
D. A. Tverdyi, R. I. Parovik, “Investigation of Finite-Difference Schemes for the Numerical Solution of a Fractional Nonlinear Equation”, Fractal and Fractional, 6:1 (2022), 23
D. A. Tverdyi, R. I. Parovik, “Application of the Fractional Riccati Equation for Mathematical Modeling of Dynamic Processes with Saturation and Memory Effect”, Fractal and Fractional, 6:3 (2022), 163
D. A. Tverdyi, E. O. Makarov, R. I. Parovik, “Hereditary Mathematical Model of the Dynamics of Radon Accumulation in the Accumulation Chamber”, Mathematics, 11:4 (2023), 850
D. A. Tverdyi, R. I. Parovik, “Hybrid GPU–CPU Efficient Implementation of a Parallel Numerical Algorithm for Solving the Cauchy Problem for a Nonlinear Differential Riccati Equation of Fractional Variable Order”, Mathematics, 11:15 (2023), 3358
D. A. Tverdyi, R. I. Parovik, E. O. Makarov, “Estimation of radon flux density changes in temporal vicinity of the Shipunskoe earthquake with $M_w=7.0$, 17 August 2024 with the use of the hereditary mathematical model”, Geosciences, 15:1 (2025), 30
D. A. Tverdyi, R. I. Parovik, “Inverse problem on determining variable-order fractional derivative in mathematical model of anomalous variations in radon volumetric activity”, News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 27:6 (2025), 77–88
2.
D. A. Tvyordyj, “Analysis of efficiency of the hybrid parallel algorithm for numerical solution of the cauchy problem for hereditary models of radon volumetric activity in FEVO software complex”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 50:1 (2025), 149–168
2024
3.
D. A. Tvyordyj, E. O. Makarov, “Some aspects of the implementation of the PRPHMM 1.0 software package for refining the parameters of hereditary mathematical models of radon transfer in a storage chamber”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 49:4 (2024), 135–156
4.
D. A. Tvyordyj, E. O. Makarov, R. I. Parovik, “Identification of parameters of the mathematical $\alpha$-model of radon transport in the accumulation chamber based on data from the Karymshina site in Kamchatka”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 48:3 (2024), 95–119
D. A. Tvyordyj, R. I. Parovik, “The optimization problem for determining the functional dependence of the variable order of the fractional derivative of the Gerasimov-Caputo type”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 47:2 (2024), 35–57
D. A. Tvyordyj, R. I. Parovik, “Application of high-performance computing to solve the cauchy problem with the fractional Riccati equation using an nonlocal implicit finite-difference scheme”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 46:1 (2024), 103–117
D. A. Tverdyi, “Restoration of the order of fractional derivative
in the problem of mathematical modelling of radon accumulation
in the excess volume of the storage chamber based
on the data of Petropavlovsk-Kamchatsky geodynamic polygon”, News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 2023, no. 6, 83–94
D. A. Tvyordyj, R. I. Parovik, “Solution of the inverse problem of identifying the order of the fractional derivative in a mathematical model of the dynamics of solar activitythe at rising phase”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 45:4 (2023), 36–51
D. A. Tvyordyj, E. I. Malkin, “Computer simulation of the propagation of a plane electromagnetic wave in a waveguide formed by the Earth's surface and the ionosphere under the condition of inhomogeneous boundary conductivity”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 44:3 (2023), 104–120
10.
D. A. Tvyordyj, E. O. Makarov, R. I. Parovik, “Research of stress-strain state of geo-environment by emanation methods on the example of $\alpha$(t)-model of radon transport”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 44:3 (2023), 86–104
D. A. Tvyordiy, R. I. Parovik, A. R. Hayotov, A. K. Boltaev, “Parallelization of a numerical algorithm for solving the Сauchy problem for a nonlinear differential equation of fractional variable order using OpenMP technology”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 43:2 (2023), 87–110
D. A. Tvyordyj, E. I. Malkin, R. I. Parovik, “Mathematical modeling of the propagation of a plane electromagnetic wave in a strip waveguide with inhomogeneous boundary conductivity”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 41:4 (2022), 66–88
13.
D. A. Tvyordyj, R. I. Parovik, “Mathematical modeling in matlab of solar activity cycles according to the growth-decline of the Wolf number”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 41:4 (2022), 47–64
D. A. Tvyordyj, R. I. Parovik, “Fractional differential model of physical processes with saturation and its application to the description of the dynamics of COVID-19”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 40:3 (2022), 119–136
2020
15.
D. A. Tvyordy, “The nonlocal Koshy problem for the Riccati equation
of the fractional order as a mathematical model
of dynamics of solar activity”, News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 2020, no. 1, 57–62
D. A. Tvyordyj, “Hereditary Riccati Equation with Fractional Derivative of Variable Order”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 154 (2018), 105–112; J. Math. Sci. (N. Y.), 253:4 (2021), 564–572
D. A. Tvyordyj, “The Cauchy problem for the Riccati equation with variable power memory and non-constant coeffcients”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, no. 3(23), 148–157
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