Alexander Zlotnik

2024¹

2023⁷

• Article Zlotnik A. Conditions for L² -dissipativity of an explicit symmetric finite-difference scheme for linearized 2D and 3D gas dynamics equations with a regularization // Discrete and Continuous Dynamical Systems - Series B. 2023. Vol. 28. No. 3. P. 1571-1589. doi
• Article Zlotnik A., Čiegis R. On Construction and Properties of Compact 4th Order Finite-Difference Schemes for the Variable Coefficient Wave Equation // Journal of Scientific Computing. 2023. Vol. 95. No. 1. Article 3. doi
• Article Zlotnik A., Lomonosov T. On Regularized Systems of Equations for Gas Mixture Dynamics with New Regularizing Velocities and Diffusion Fluxes // Entropy. 2023. Vol. 25. No. 1. Article 158. doi
• Article Zlotnik A., Lomonosov T. On a doubly reduced model for dynamics of heterogeneous mixtures of stiffened gases, its regularizations and their implementations // Chaos. 2023. Vol. 33. No. 11. Article 113128. doi
• Article A. A. Zlotnik, Chetverushkin B. Properties and errors of second-order parabolic and hyperbolic perturbations of a first-order symmetric hyperbolic system / Пер. с рус. // Sbornik Mathematics. 2023. Vol. 214. No. 4. P. 444-478. doi
• Article Zlotnik A., Lomonosov T. Regularized Equations for Dynamics of the Heterogeneous Binary Mixtures of the Noble-Abel Stiffened-Gases and Their Application / Пер. с рус. // Doklady Mathematics. 2023. Vol. 108. No. 3. P. 443-449. doi
• Article Zlotnik A. Remarks on the model of quasi-homogeneous binary mixtures with the NASG equations of state // Applied Mathematics Letters. 2023. Vol. 146. Article 108801. doi

2022⁸

• Article Zlotnik A.A. Conditions for Dissipativity of an Explicit Finite-Difference Scheme for a Linearized Multidimensional Quasi-Gasdynamic System of Equations / Пер. с рус. // Doklady Mathematics. 2022. Vol. 106. No. 1. P. 236-242. doi
• Article Zlotnik A., Fedchenko A., Lomonosov T. Entropy Correct Spatial Discretizations for 1D Regularized Systems of Equations for Gas Mixture Dynamics // Symmetry. 2022. Vol. 14. No. 10. Article 2171. doi
• Article A. A. Zlotnik, T. A. Lomonosov. On L^2-dissipativity of a linearized scheme on staggered meshes with a regularization for 1D barotropic gas dynamics equations / Пер. с рус.: A. A. Zlotnik, T. A. Lomonosov. // Computational Mathematics and Mathematical Physics. 2022. Vol. 62. No. 11. P. 1817-1837. doi
• Article A. A. Zlotnik, Chetverushkin B. N. On Second-Order Parabolic and Hyperbolic Perturbations of a First-Order Hyperbolic System / Пер. с рус. // Doklady Mathematics. 2022. Vol. 106. No. 2. P. 308-314. doi
• Article Zlotnik A., Čiegis R. On higher-order compact ADI schemes for the variable coefficient wave equation // Applied Mathematics and Computation. 2022. Vol. 412. Article 126565. doi
• Article Zlotnik A., Fedchenko A. On properties of aggregated regularized systems of equations for a homogeneous multicomponent gas mixture // Mathematical Methods in the Applied Sciences. 2022. Vol. 45. No. 15. P. 8906-8927. doi
• Article Zlotnik A.A. On the Construction of Regularized Equations of Motion for a Mixture of Viscous Incompressible Fluids / Пер. с рус. // Doklady Mathematics. 2022. Vol. 106. No. 2. P. 380-385. doi
• Article Zlotnik A.A., Fedchenko A.S. On the properties of a quasihydrodynamic system of equations for a homogeneous gas mixture with a common regularizing velocity / Пер. с рус. // Differential Equations. 2022. Vol. 58. No. 3. P. 341-356. doi

2021⁸

• Article Zlotnik A., Čiegis R. A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes // Applied Mathematics Letters. 2021. Vol. 115. Article 106949. doi
• Article Balashov V., Zlotnik A. Correction to the paper: An energy dissipative spatial discretization for the regularized compressible Navier-Stokes-Cahn-Hilliard system of equations (in math. model. anal., 25(1): 110–129) // Mathematical Modelling and Analysis. 2021. Vol. 26. No. 2. P. 337-338. doi
• Article Zlotnik A.A., Lomonosov T.A. L^2-Dissipativity of Difference Schemes for Regularized 1D Barotropic Gas Dynamic Equations at Low Mach Numbers / Пер. с рус. // Mathematical Models and Computer Simulations. 2021. Vol. 13. No. 6. P. 1097-1108. doi
• Article Zlotnik A. On Conditions for L2-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations // Symmetry. 2021. Vol. 13. No. 11. Article 2184. doi
• Article Balashov V., Zlotnik A. On a new spatial discretization for a regularized 3D compressible isothermal Navier–Stokes–Cahn–Hilliard system of equations with boundary conditions // Journal of Scientific Computing. 2021. Vol. 86. Article 33. doi
• Article Zlotnik A., Kireeva O. On compact 4th order finite-difference schemes for the wave equation // Mathematical Modelling and Analysis. 2021. Vol. 26. No. 3. P. 479-502. doi
• Article Zlotnik A.A., Fedchenko A.S. Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture / Пер. с рус. // Doklady Mathematics . 2021. Vol. 104. No. 3. P. 340-346. doi
• Article Zlotnik A., Chetverushkin B. Spectral stability conditions for an explicit three-level finite-difference scheme for a multidimensional transport equation with perturbations / Пер. с рус. // Differential Equations. 2021. Vol. 57. No. 7. P. 891-900. doi

2020⁹

• Article Balashov V., Zlotnik A. An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier–Stokes–Cahn–Hilliard equations // Journal of Computational Dynamics. 2020. Vol. 7. No. 2. P. 291-312. doi
• Article Balashov V., Zlotnik A. An energy dissipative spatial discretization for the regularized compressible Navier-Stokes-Cahn-Hilliard system of equations // Mathematical Modelling and Analysis. 2020. Vol. 25. No. 1. P. 110-129. doi
• Article Zlotnik A.A., Zlotnik I.A. Fast Fourier solvers for the tensor product high-order FEM for a Poisson type equation / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2020. Vol. 60. No. 2. P. 240-257. doi
• Article Zlotnik A., Lomonosov T. L^2-dissipativity of the linearized explicit finite-difference scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations // Applied Mathematics Letters. 2020. Vol. 103. Article 106198. doi
• Article Zlotnik A.A., Lomonosov T.A. On L^2-dissipativity of a linearized explicit finite-difference scheme with quasi-gas dynamic regularization for the barotropic gas dynamics system of equations / Пер. с рус. // Doklady Mathematics. 2020. Vol. 101. No. 3. P. 198-204. doi
• Article Elizarova T., Zlotnik A. On aggregated regularized equations for homogeneous binary gas mixture flows with viscous compressible components // AIP Conference Proceedings. 2020. Vol. 2293. No. 1. P. 210016-1-210016-4. doi
• Chapter Zlotnik A. On enlarged sufficient conditions for L^2-dissipativity of linearized explicit schemes with regularization for 1D gas dynamics systems of equations, in: Differential and Difference Equations with Applications. ICDDEA 2019, Lisbon, Portugal, July 1–5 Vol. 333. Springer, 2020. doi P. 53-67. doi
• Article Zlotnik A.A., Chetverushkin B. Stability of implicit difference schemes for a linearized hyperbolic quasi-gasdynamic system of equations / Пер. с рус. // Differential Equations. 2020. Vol. 56. No. 7. P. 910-922. doi
• Article Zlotnik A. A., Chetverushkin B. N. Stability of numerical methods for solving second-order hyperbolic equations with a small parameter / Пер. с рус. // Doklady Mathematics. 2020. Vol. 101. No. 1. P. 30-35. doi

2019⁵

• Article Zlotnik A.A., Lomonosov T.A. Conditions for L^2-Dissipativity of Linearized Explicit Difference Schemes with Regularization for 1D Barotropic Gas Dynamics Equations / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2019. Vol. 59. No. 3. P. 452-464. doi
• Article Balashov V., Savenkov E., Zlotnik A. Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics // Russian Journal on Numerical Analysis and Mathematical Modelling. 2019. Vol. 34. No. 1. P. 1-13. doi
• Article Zlotnik A. On L^2-dissipativity of linearized explicit finite-difference schemes with a regularization on a non-uniform spatial mesh for the 1D gas dynamics equations // Applied Mathematics Letters. 2019. Vol. 92. P. 115-120. doi
• Article Elizarova T. G., Zlotnik A.A., Shil’nikov E. V. Regularized Equations for Numerical Simulation of Flows of Homogeneous Binary Mixtures of Viscous Compressible Gases / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2019. Vol. 59. No. 11. P. 1832-1847. doi
• Article Zlotnik A., Lomonosov T. Verification of an Entropy Dissipative QGD-Scheme for the 1D Gas Dynamics Equations // Mathematical Modelling and Analysis. 2019. Vol. 24. No. 2. P. 179-194. doi

2018⁹

• Article Zlotnik A., Čiegis R. A "converse'' stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation // Applied Mathematics Letters. 2018. Vol. 80. P. 35-40. doi
• Article Trautmann P., Vexler B., Zlotnik A. Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients // Mathematical Control and Related Fields. 2018. Vol. 8. No. 2. P. 411-449. doi
• Article Elizarova T.G., Zlotnik A.A., Istomina M. Hydrodynamical aspects of the formation of spiral–vortical structures in rotating gaseous disks / Пер. с рус. // Astronomy Reports. 2018. Vol. 62. No. 1. P. 9-18. doi
• Article Vexler B., Zlotnik A., Trautmann P. On a finite element method for measure-valued optimal control problems governed by the 1D generalized wave equation // Comptes Rendus Mathematique. 2018. Vol. 356. No. 5. P. 523-531. doi
• Article Chetverushkin B. N., Zlotnik Alexander A. On a hyperbolic perturbation of a parabolic initial-boundary value problem // Applied Mathematics Letters. 2018. Vol. 83. P. 116-122. doi
• Article Zlotnik A., Lomonosov T. On conditions for L2-dissipativity of linearized explicit QGD finite-difference schemes for one-dimensional gas dynamics equations / Пер. с рус. // Doklady Mathematics. 2018. Vol. 98. No. 2. P. 458-463. doi
• Chapter Zlotnik A., Lomonosov T. On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations, in: Differential and Difference Equations with Applications Vol. 230. Springer, 2018. doi P. 635-647. doi
• Article Zlotnik A. On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier-Stokes systems of equations in polar coordinates // Russian Journal on Numerical Analysis and Mathematical Modelling. 2018. Vol. 33. No. 3. P. 199-210. doi
• Article Zlotnik A., Kireeva O. Practical error analysis for the bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data // Mathematical Modelling and Analysis. 2018. Vol. 23. No. 3. P. 359-378. doi

2017⁶

• Article Zlotnik A.A., Zlotnik I.A. A Fast Direct Algorithm for Implementing a High-Order Finite Element Method on Rectangles as Applied to Boundary Value Problems for the Poisson Equation / Пер. с рус. // Doklady Mathematics. 2017. Vol. 95. No. 2. P. 129-135. doi
• Article Balashov V., Zlotnik Alexander, Savenkov E. Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface // Russian Journal on Numerical Analysis and Mathematical Modelling. 2017. Vol. 32. No. 6. P. 347-358. doi
• Article Zlotnik A. A., Chetverushkin B. N. Entropy Balance for the One-Dimensional Hyperbolic Quasi-Gasdynamic System of Equations / Пер. с рус. // Doklady Mathematics. 2017. Vol. 95. No. 3. P. 276-281. doi
• Article A.A. Zlotnik. Entropy-Conservative Spatial Discretization of the Multidimensional Quasi-Gasdynamic System of Equations / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2017. Vol. 57. No. 4. P. 706-725. doi
• Article Chetverushkin B. N., Zlotnik A.A. On some properties of multidimensional hyperbolic quasi-gasdynamic systems of equations // Russian Journal of Mathematical Physics. 2017. Vol. 24. No. 3. P. 299-309. doi
• Chapter Zlotnik Alexander. Well-posedness of the IBVPs for the 1D viscous gas equations, in: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Cham, Switzerland: Springer, 2017. doi P. 1-73. doi

2016⁴

• Article A.A. Zlotnik. On Conservative Spatial Discretizations of the Barotropic Quasi-Gasdynamic System of Equations with a Potential Body Force / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2016. Vol. 56. No. 2. P. 303-319. doi
• Article A.A. Zlotnik. On New Spatial Discretization of the Multidimensional Quasi-Gasdynamic System of Equations with Nondecreasing Total Entropy / Пер. с рус. // Doklady Mathematics. 2016. Vol. 94. No. 1. P. 423-429. doi
• Chapter Zlotnik Alexander, Gavrilin Vladimir. On a conservative finite-difference method for 1D shallow water flows based on regularized equations, in: Mathematical Problems in Meteorological Modelling. Mathematics in Industry Vol. 24. Berlin : Springer, 2016. doi P. 3-18. doi
• Article Zlotnik Alexander, Zlotnik Ilya. Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis // Russian Journal on Numerical Analysis and Mathematical Modelling. 2016. Vol. 31. No. 1. P. 51-64. doi

2015⁷

• Chapter Zlotnik A. Error Estimates of the Crank-Nicolson-Polylinear FEM with the Discrete TBC for the Generalized Schrödinger Equation in an Unbounded Parallelepiped, in: Finite Difference Methods, Theory and Applications 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Revised Selected Papers Vol. 9045. Zürich : Springer, 2015. doi P. 129-141. doi
• Article Zlotnik A., Romanova A. On a Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip // Applied Numerical Mathematics. 2015. Vol. 93. P.  279-294. doi
• Article Ducomet Bernard, Zlotnik Alexander, Romanova Alla. On a splitting higher-order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped // Applied Mathematics and Computation. 2015. Vol. 255. P. 195-206. doi
• Article V.A. Gavrilin, A.A. Zlotnik. On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2015. Vol. 55. No. 2. P. 264-281. doi
• Chapter Zlotnik Alexander, Ducomet Bernard, Zlotnik Ilya, Romanova Alla. Splitting in Potential Finite-Difference Schemes with Discrete Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation, in: Numerical Mathematics and Advanced Applications - ENUMATH 2013 Vol. 103. Springer, 2015. P. 203-211. doi
• Article Zlotnik Alexander, Zlotnik Ilya. The High Order Method with Discrete TBCs for Solving the Cauchy Problem for the 1D Schrὅdinger Equation // Computational Methods in Applied Mathematics. 2015. Vol. 15. No. 2. P. 233-245. doi
• Article Zlotnik Alexander. The Numerov-Crank-Nicolson Scheme on a Non-Uniform Mesh for the Time-Dependent Schrödinger Equation on the Half-Axis // Kinetic and Related Models. 2015. Vol. 8. No. 3. P. 587-613. doi

2014²

• Article Elizarova T.G., Zlotnik A.A., Chetverushkin B. N. On quasi-gasdynamic and quasi-hydrodynamic equtions for binary mixtures of gases / Пер. с рус. // Доклады Академии наук. 2014. Vol. 90. No. 3. P. 1-5. doi
• Article Ducomet Bernard, Zlotnik Alexander, Zlotnik Ilya. The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip // ESAIM: Mathematical Modelling and Numerical Analysis. 2014. Vol. 48. No. 6. P. 1681-1699. doi

2013²

• Article Zlotnik A., Koltsova N. A family of finite-difference schemes with discrete transparent boundary conditions for a parabolic equation on the half-axis // Computational Methods in Applied Mathematics. 2013. Vol. 13. No. 2. P. 119-138. doi
• Article Zlotnik Alexander, Ducomet B. On a regularization of the magnetic gas dynamics system of equations // Kinetic and Related Models. 2013. Vol. 6. No. 3. P. 533-543. doi

2012⁴

• Article Zlotnik A.A., Zlotnik I. A. Finite element method with discrete transparent boundary conditions for the one-dimensional nonstationary 1D Schrödinger equation / Пер. с рус. // Доклады Академии наук. 2012. Vol. 86. No. 3. P. 750-755. doi
• Article Zlotnik A., Zlotnik I. A. Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation // Kinetic and Related Models. 2012. Vol. 5. No. 3. P. 639-667. doi
• Article Zlotnik A.A. Spatial discretization of one-dimensional quasi-gasdynamic systems of equations and the entropy and energy balance equations / Пер. с рус. // Доклады Академии наук. 2012. Vol. 86. No. 1. P. 464-468. doi
• Article Zlotnik A.A. Spatial discretization of the one-dimensional quasi-gasdynamic system of equations and the entropy balance equation / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2012. Vol. 52. No. 7. P. 1060-1071. doi

2011¹

2010⁴

• Article Zlotnik A. Linearized stability of equilibrium solutions to the quasi-gasdynamic system of equations / Пер. с рус. // Doklady Mathematics. 2010. Vol. 82. No. 2. P. 811-815. doi
• Article Zlotnik A. Quasi-gasdynamic system of equations with general equations of state / Пер. с рус. // Doklady Mathematics. 2010. Vol. 81. No. 2. P. 312-316. doi
• Article Zlotnik A., Lapukhina A. Stability of a Numerov type finite–difference scheme with approximate transparent boundary conditions for the nonstationary Schrödinger equation on the half-axis / Пер. с рус. // Journal of Mathematical Sciences. 2010. Vol. 169. No. 1. P. 84-97. doi
• Article Zlotnik A. Stability of small perturbations for a modified two-dimensional quasi-gasdynamic model of traffic flows / Пер. с рус. // Mathematical Models and Computer Simulations. 2010. Vol. 2. No. 6. P. 776-781. doi

2009⁴

• Article Zlotnik A., Kireeva O. Error bounds for FEM with generalized cubic splines // Computational Methods in Applied Mathematics. 2009. Vol. 9. No. 2. P. 203-218. doi
• Article Zlotnik Alexander, Ducomet B., Zlotnik I. On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation // Kinetic and Related Models. 2009. Vol. 2. No. 1. P. 151-179. doi
• Article Zlotnik A., Ducomet B., Goutte H., Berger J. On one semidiscrete Galerkin method for a generalized time-dependent 2D Schrödinger equation // Applied Mathematics Letters. 2009. No. 22. P. 252-257. doi
• Article Zlotnik A., Ducomet B., Goutte H., Berger J. On one version of a semidiscrete Galerkin method for PDE problems involving a 2D Hamiltonian operator // Communications in Mathematical Sciences. 2009. Vol. 7. No. 2. P. 247-295. doi