Computer algebra, partial differential equation, generation of difference schemes.
Main publications:
V. P. Gerdt, Yu. A. Blinkov, “Involutive divisions of monomials”, Programming and Computer Software, 24:6 (1998), 283–285
V. P. Gerdt, Yu. A. Blinkov, “Involutive Bases of Polynomial Ideals”, Mathematics and Computers in Simulation, 45:5-6 (1998), 519–541
V. P. Gerdt, Yu. A. Blinkov, “Minimal Involutive Bases”, Mathematics and Computers in Simulation, 45 (1998), 543–560
V. P. Gerdt, Yu. A. Blinkov, V. V Mozzhilkin, “Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations”, Symmetry, Integrability and Geometry: Methods and Applications, 2 (2006), Paper 051, 26 pp. ; http://www.emis.de/journals/SIGMA/2006/Paper051/index.html
V. P. Gerdt, Yu. A. Blinkov, “Specialized Computer Algebra System GINV”, Programming and Computer Software, 34:2 (2008), 112–123
L. I. Mogilevich, Yu. A. Blinkov, E. V. Popova, V. S. Popov, “Solitary deformation waves in two coaxial shells made of material with combined nonlinearity and forming the walls of annular and circular cross-section channels filled with viscous fluid”, Izvestiya VUZ. Applied Nonlinear Dynamics, 32:4 (2024), 521–540
2023
2.
R. È. Bairamov, Yu. A. Blinkov, I. V. Levichev, M. D. Malykh, V. S. Melezhik, “Analytical study of cubature formulas on a sphere in computer algebra systems”, Zh. Vychisl. Mat. Mat. Fiz., 63:1 (2023), 93–101; Comput. Math. Math. Phys., 63:1 (2023), 77–85
Yu. A. Blinkov, M. D. Malykh, L. A. Sevastianov, “On differential approximations of difference schemes”, Izv. Saratov Univ. Math. Mech. Inform., 21:4 (2021), 472–488
L. I. Mogilevich, Yu. A. Blinkov, S. V. Ivanov, “Waves of strain in two coaxial cubically nonlinear cylindrical shells with a viscous fluid between them”, Izvestiya VUZ. Applied Nonlinear Dynamics, 28:4 (2020), 435–454
5.
L. I. Mogilevich, S. V. Ivanov, Yu. A. Blinkov, “Modeling of Nonlinear Waves in Two Coaxial Physically Nonlinear Shells with a Viscous Incompressible Fluid Between Them, Taking into Account the Inertia of its Motion”, Rus. J. Nonlin. Dyn., 16:2 (2020), 275–290
2018
6.
Yu. A. Blinkov, E. V. Evdokimova, L. I. Mogilevich, “Nonlinear waves in cylinder shell containing viscous liquid, under the impact of surrounding elastic medium and structural damping in longitudinal direction”, Izvestiya VUZ. Applied Nonlinear Dynamics, 26:6 (2018), 32–47
7.
D. L. Michels, V. P. Gerdt, Yu. A. Blinkov, D. A. Lyakhov, “On the consistency analysis of finite difference approximations”, Zap. Nauchn. Sem. POMI, 468 (2018), 249–266; J. Math. Sci. (N. Y.), 240:5 (2019), 665–677
Yu. A. Blinkov, Yu. N. Kondratova, A. V. Mesyanzhin, L. I. Mogilevich, “Nonlinear waves mathematical modeling in coaxial shells filled with viscous liquid”, Izv. Saratov Univ. Math. Mech. Inform., 16:3 (2016), 331–336
9.
Yu. A. Blinkov, A. V. Mesyanzhin, L. I. Mogilevich, “Wave occurrences mathematical modeling in two geometrically nonlinear elastic coaxial cylindrical shells, containing viscous incompressible liquid”, Izv. Saratov Univ. Math. Mech. Inform., 16:2 (2016), 184–197
A. Yu. Blinkova, Yu. A. Blinkov, S. V. Ivanov, L. I. Mogilevich, “Nonlinear deformation waves in a geometrically and physically nonlinear viscoelastic cylindrical shell containing viscous incompressible fluid and surrounded by an elastic medium”, Izv. Saratov Univ. Math. Mech. Inform., 15:2 (2015), 193–202
Vladimir P. Gerdt, Yuri A. Blinkov, Vladimir V. Mozzhilkin, “Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations”, SIGMA, 2 (2006), 051, 26 pp.
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