info@viam.science.tsu.ge (+995 32) 2 30 30 40 (+995 32) 2 18 66 45

Jemal Rogava

  • Partial Differential Equations Department
    Chief Researcher
  • Office: room 215, University str.11, 0186 Tbilisi, Georgia
  • Phone: 599391181
  • E-mail: jemal.rogava@tsu.ge
  • Research fields: Computational Mathematics, Mathematical Modeling, Differential Equation, Mathematical Physics

Summary

Education
1963 - 1968, Ivane Javakhishvili Tbilisi State University, Master's/Master's equivalent in Mathematics
1982, Muskhelishvili Institute of Computational Mathematics, Doctoral/PhD, Ed.D or other equivalent in Mathematics
1995, Ivane Javakhishvili Tbilisi State University, DSc in Mathematics

work experience

15.01.1968 - 28.12.1990 -- Iv. Ilia Vekua Institute of Applied Mathematics of Javakhishvili Tbilisi State University (researcher, junior researcher, group leader)

16.01.1984 - 28.12.1990 -- Ivane Javakhishvili Tbilisi State University (teacher)

15.01.1990 - 29.12.2000 -- Technical University of Georgia (laboratory manager)

15.01.1990 - 29.12.2000 -- Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishvili Tbilisi State University (senior researcher, leading researcher)

20.01.1997 - 29.12.2006 -- Ivane Javakhishvili Tbilisi State University (Professor)

17.01.2000 - 29.12.2006 -- Ivane Javakhishvili Tbilisi State University named after Ilia Vekua Institute of Applied Mathematics (leading scientific fellow)

From 2006 until now -- Ilia Vekua Institute of Applied Mathematics of Ivane Javakhishvili Tbilisi State University (Senior, Chief Researcher)

From 2006 to the present -- Ivane Javakhishvili Tbilisi State University (Associate Professor)

Projects

Talks

  • On Convergence of a Three-Layer Semi-Discrete Scheme for the Nonlinear Dynamic String Equation of Kirchhoff-Type with Time-Dependent Coefficients, by Zurab Vashakidze (Speaker), Jemal Rogava at The Fourth International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS" Dedicated to the 105th Anniversary of I. Javakhishvili Tbilisi State University (TSU) & 55th Anniversary of I. Vekua Instit, Tbilisi, Georgia, 13-15 September, 2023.
  • Convergence and numerical experiments of a three-layer semi-discretization approach for the nonlinear Kirchhoff-type dynamic string equation with time-varying coefficients, by Zurab Vashakidze (Speaker), Jemal Rogava at XIII Annual International Conference of the Georgian Mathematical Union, Batumi, Georgia, 04-09 September, 2023.
  • On a Convergence of a Three-Layer Semi-Discrete Approach for Solving the Nonlinear Dynamic Kirchhoff-Type String Equation with Time-Varying Coefficients, by Zurab Vashakidze (Speaker), Jemal Rogava at The Tbilisi Analysis & PDE Workshop (TAPDE Workshop 2023), Tbilisi, Georgia, from 30 August to 02 September, 2023.
  • Decomposition type formulas for approximation of a cosine operator function, by Jemal Rogava (Speaker) at XXXVI International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia, 19-21 April, 2022.
  • Splitting of the four-layer semi-discrete schemes of solution the evolutionary equation with variable operator on two-level schemes, by David Gulua (Speaker), Jemal Rogava at XXXV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia, 21-23 April, 2021.
  • On the convergence of the symmetrical, semi-discrete scheme for the nonlinear Charney-Obukhov differential equation, by Jemal Rogava (Speaker), Mikheil Tsiklauri at XXXV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics of Ivane Javakhisvili Tbilisi State University, Tbilisi, Georgia, 21-23 April, 2021.
  • On the convergence of an iterative method for one non-linear operator equation, by Jemal Rogava (Speaker), Mikheil Tsiklauri at XXXIV International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia, 16-19 September, 2020.
  • On stability and convergence of threelayer semi-discrete scheme for nonlinear second order evolution equation, by Jemal Rogava (Speaker) at The Fourth International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering. AMINSE 2019, Tbilisi, Georgia, 23-26 September, 2019.
  • On the stability of bijection in the Banach space in case of non-linear perturbation, by Jemal Rogava (Speaker) at XXXIII International Enlarged Sessions of the Seminar of Ilia Vekua Institute of Applied Mathematics, Tbilisi, Georgia, 23-25 April, 2019.
  • Decomposition Formulas for Cosine Operator Function with Two and Multi-addend Argument, by Jemal Rogava (Speaker), Nana Dikhaminjia, Mikheil Tsiklauri at The Third International Conference "MODERN PROBLEMS IN APPLIED MATHEMATICS" Dedicated to the Centenary of I.Javakhishvili Tbilisi State University (TSU) & 50th Anniversary of I.Vekua Institute of Appl, Tbilisi, Georgia, 19-21 September, 2018.
  • Nonlinear dynamics of the solitary vortices and the wave structures in the complex media, by Khatuna Elbakidze (Speaker), Jemal Rogava, Oleg Kharshiladze at 4th International Conference on Physics, Berlin, Germany, 17-19 September, 2018.
  • Parallel Type of Decomposition Scheme for Quasilinear Abstract Hyperbolic Equation, by Nana Dikhaminjia (Speaker), Jemal Rogava, Mikheil Tsiklauri at 3rd International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering Dedicated to the 80th Birthday of Professor David Gordeziani, Tbilisi, Georgia, 06-09 December, 2017.
  • Variational-Difference Scheme for Kirchhoff Two-Dimensional Nonlinear Dynamical Equation. , by Zurab Vashakidze (Speaker), Jemal Rogava, Archil Papukashvili at VIII Annual International Conference of the Georgian Mathematical Union., Batumi, Georgia, 04-08 September, 2017.
  • On the numerical solution of contact problem for Poissons and Kirchhoff equation system , by Archil Papukashvili (Speaker), Jemal Rogava, Zurab Vashakidze at V Annual Meeting of the Georgian Mechanical Union, Tbilisi Georgia, 08-10 October, 2014.
  • Construction of High Order Accuracy Decomposition Scheme for an Abstract Hyperbolic Equation with the Lipschitz Continuous Operator on the Basis of Rational Splitting of the Cosine-Operator Function, by Jemal Rogava (Speaker), Mikheil Tsiklauri at 9th International Conferenceof Numerical Analysis and Applied Mathematics, Halkidiki, Greece, 19-25 September, 2011.
  • Construction and Numerical Realization of Decomposition Schemefor Multidimensional Quasi-Linear Evolution Equation, by Jemal Rogava (Speaker), Nana Dikhaminjia, Mikheil Tsiklauri at 9th International Conferenceof Numerical Analysis and Applied Mathematics, Halkidiki, Greece, 19-25 September, 2011.
  • Numerical Investigation of Spilled Oil Spreading Into Soil for Underground Water Pollution Risk Assessment, by Teimurazi Davitashvili (Speaker), Nana Dikhaminjia, Jemal Rogava, Mikheil Tsiklauri at II International Conference Dedicated to the 70th Anniversary of the Georgian National Academy of Sciences & the 120th Birthday of its First President Academician Nikoloz (Niko) Muskhelisxhvili, Batumi, Georgia, 15-19 September, 2011.

Publications

  • Jemal Rogava, Zurab Vashakidze, On convergence of a three-layer semi-discrete scheme for the non-linear dynamic string equation of Kirchhoff-type with time-dependent coefficients, Z Angew Math Mech. (ZAMM) e202300608, John Wiley & Sons, Inc., 2024.
  • Jemal Rogava, Zurab Vashakidze, On Convergence of a Three-Layer Semi-Discrete Scheme for the Nonlinear Dynamic String Equation of Kirchhoff-Type with Time-Dependent Coefficients, arXiv preprint arXiv:2303.10350, arXiv, 2023.
  • Jemal Rogava, Mikheil Tsiklauri, Zurab Vashakidze, On stability and convergence of a three-layer semi-discrete scheme for an abstract analogue of the Ball integro-differential equation, Journal of Mathematical Analysis and Applications, Volume 518, Issue 1, Elsevier, 2022.
  • Jemal Rogava, Mikheil Tsiklauri, Zurab Vashakidze, On Stability and Convergence of a Three-layer Semi-discrete Scheme for an Abstract Analogue of the Ball Integro-differential Equation, arXiv:2201.12345, arXiv, 2022.
  • Jemal Rogava, On the approximation of a semi-group of operators using fractional-linear operator functions and weighted means, Functional Analysis and Its Applications, Vol. 56(2), 47-63, Springer, 2022.
  • Nana Dikhaminjia, Jemal Rogava, Mikheil Tsiklauri, A parallel type decomposition scheme for quasi-linear abstract hyperbolic equation, Georgian Mathematical Journal, Walter De Gruyter GmbH, 2022.
  • David Gulua, Jemal Rogava, Reduction of a Four-Layer Semi-Discrete Scheme for an Abstract Evolution Equation to Two-Layer Schemes and Estimation of the Approximate Solution Errors by Using Associated Polynomials, BULLETIN OF THE GEORGIAN NATIONAL ACADEMY OF SCIENCES, vol. 15(2), , 2021.
  • Romeo Galdava, David Gulua, Jemal Rogava, Study of Three-Layer Semi-Discrete Schemes for Second Order Evolution Equations by Chebyshev Polynomials, In: Jaiani, G., Natroshvili, D. (eds) Applications of Mathematics and Informatics in Natural Sciences and Engineering. AMINSE 2019. Springer Proceedings in Mathematics & Statistics, vol 334, pp 153–196, Springer, Cham, 2020.
  • Nana Dikhaminjia, Jemal Rogava, Mikheil Tsiklauri, Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation, Georgian Mathematical Journal, vol. 25, no. 3, pp. 337-348, Walter De Gruyter GmbH, 2018.
  • David Gulua, Jemal Rogava, The perturbation algorithm for the realization of a four-layer semi-discrete solution scheme of an abstract evolutionary problem, Georgian Mathematical Journal, 25(1), pp. 77-92, Walter de Gruyter GmbH, 2018.
  • Jemal Rogava, David Gulua, Romeo Galdava, Reduction of Some Semi-discrete Schemes for an Evolutionary Equation to Two-Layer Schemes and Estimates for the Approximate Solution Error, In: Falcone, G. (eds) Lie Groups, Differential Equations, and Geometry. UNIPA Springer Series, pp 223–246, Springer, Cham, 2017.
  • David Gulua, Jemal Rogava, On the perturbation algorithm for the semi-discrete scheme for the evolution equation and estimation of the approximate solution error using semigroups, Computational Mathematics and Mathematical Physics, volume 56, Issue 7, pp 1269–1292, , 2016.
  • Archil Papukashvili, Jemal Rogava, Zurab Vashakidze, On one numerical method of research of the stress-deformed condition of some multystructures with difficult geometry , TICSSAM-2015, March 21-23, 2015,Tbilisi. Conference’s Proceedings, p.140-146, Sokhumi University Press, 2015.
  • Nana Dikhaminjia, Mikheil Tsiklauri, Jemal Rogava, Fast approximation of sine and cosine hyperbolic functions for the calculation of the transmission matrix of a multiconductor transmission line, IEEE Transactions on Electromagnetic Compatibility 57.6, , 2015.
  • Nana Dikhaminjia, Jemal Rogava, Mikheil Tsiklauri, Construction and Investigation of a Fourth Orderof Accuracy Decomposition Schemefor Nonhomogeneous Multidimensional Hyperbolic Equation, Numerical Functional Analysis and Optimization, Volume 35, Issue 3,p. 275-293, , 2014.
  • David Gulua, Jemal Rogava, Perturbation algorithm for implementing a finite difference approximation to an abstract evolutionary problem and explicit error estimation of its solution, Doklady Mathematics, Volume 89, Issue 3, pp 335–337, , 2014.
  • Jemal Rogava, Mikheil Tsiklauri, Convergence of a semi-discrete scheme for an abstract nonlinear second order evolution equation, Applied Numerical Mathematics Volume75, Pages 22-36, , 2014.
  • Jemal Rogava, Mikheil Tsiklauri, On local convergence of a symmetric semi-discrete scheme for an abstract analogue of the Kirchhoff equation, Journal of Computational and Applied Mathematics Volume 236, Issue 15, Pages 3654-3664, , 2012.
  • Giorgi Aburjania, Jemal Rogava, Oleg Kharshiladze, Nonlinear dynamics of drift structures in a magnetized dissipative plasma, Plasma Physics Reports, Volume 37, Issue 6, pp 477–497, , 2011.
  • Jemal Rogava, Mikheil Tsiklauri, Construction of high order accuracy decomposition scheme for an abstract hyperbolic equation with the lipschitz continuous operator on the basis of rational splitting of the cosine operator function, AIP Conference Proceedings, Volume 1389, Issue 1, , 2011.
  • Jemal Rogava, Mikheil Tsiklauri, High order accuracy splitting formulas for cosine operator function and their applications, Applied Mathematics, Informatics and Mechanics (AMIM), vol. 15, no. 2, pp. 45-55, , 2010.
  • Jemal Rogava, Mikheil Tsiklauri, Semi-discrete scheme and uniqueness theorem for Charney-Obukhov nonlinear equation, Proceedings of I. Vekua Institute of Applied Mathematics, vol. 59-60,pp. 43-59, , 2010.
  • Archil Papukashvili, Jemal Peradze, Jemal Rogava, An approximate algorithm for a Kirchhoff nonlinear dynamic beam equation , Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics. v.23, Tbilisi 2009. p. 84-86. , Tbilisi University Press , 2009.
  • Jemal Rogava, Mikheil Tsiklauri, Integral semi-discrete scheme for a Kirchhoff type abstract equation with the general nonlinearity, Applied Mathematics, Informatics and Mechanics (AMIM), vol. 15, no. 2, pp. 45-55, , 2009.
  • Jemal Rogava, Mikheil Tsiklauri, The fourth order of accuracy decomposition scheme for abstract hyperbolic equation, Georgian Mathematical Journal, Volume 15, Issue 1, Pages 165–175, , 2008.
  • Jemal Rogava, Mikheil Tsiklauri, The fourth order of accuracy decomposition scheme for nonhomogeneous multidimensional hyperbolic equation, Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics. AIP Conference Proceedings, Vol. 1048,pp. 454-457, , 2008.
  • Tamaz Kaladze, Oleg Pokhotelov, Lennart Stenflo, Jemal Rogava, Luba Tsamalashvili, Mikheil Tsiklauri, Zonal flow interaction with Rossby waves in the Earth's atmosphere: A numerical simulation, Physics Letters A, Vol: 372, Issue: 31, Page: 5177-5180, Elsevier, 2008.
  • Tamaz Kaladze, Jemal Rogava, Luba Tsamalashvili, Mikheil Tsiklauri, Implicit difference scheme for the numerical resolution of the Charney-Obukhov equation with variable coefficients, Bulletin of TICMI, v. 11, 31-37, 2007, Tbilisi University Press, 2007.
  • Jemal Rogava, Mikheil Tsiklauri, High order accuracy decomposition schemes for evolution problem, Lecture Notes of TICMI, Vol. 7, p.164, , 2006.
  • Jemal Rogava, Mikheil Tsiklauri, An automatically stable and order three split rational approximation of a semigroup, Georgian Mathematical Journal, Volume 13, Issue 2, Pages 343–362, , 2006.
  • Tamaz Kaladze, Jemal Rogava, Luba Tsamalashvili, Mikheil Tsiklauri, First- and second-order accurate implicit difference schemes for the numerical resolution of the generalized Charney–Obukhov and Hasegawa–Mima equations, Journal of Plasma Physics ,Volume 72,Issue 6,December 2006 , pp.1045 - 1048, Cambridge University Press, 2006.
  • Jemal Rogava, Mikheil Tsiklauri, Investigation and numerical resolution of Initial boundary value problem for the generalized Charney-Obukhovand Hasageva-Mima equations, Physics Letters A,vol.343,pp.199-215, , 2005.
  • Jemal Rogava, Mikheil Tsiklauri, Tamar Lomtadze, Approximate solution of Cauchy problem for abstract hyperbolic equation using unitary group approximation method, Proceedings of I. Vekua Institute of Applied Mathematics, Vol. 54-55, pp.55-64, , 2005.
  • Tamaz Kaladze, Jemal Rogava, Luba Tsamalashvili, Mikheil Tsiklauri, Investigation and numerical resolution of initial-boundary value problem for the generalized Charney–Obukhov and Hasagewa–Mima equations, Physics Letters A,Vol: 343, Issue: 1, Page: 199-215, Elsevier, 2005.
  • Jemal Rogava, Luba Tsamalashvili, Mikheil Tsiklauri, Tamaz Kaladze, First and second-order accurate implicit difference schemes for the Carney-Obukhov equation, Physics Letters A, Vol. 328/1, pp.51-64, Elsevier, 2004.
  • Jemal Rogava, Mikheil Tsiklauri, Zurab Gegechkori, The fourth order accuracy decomposition scheme for an evolution problem, Paris, ESAIM-Mathematical Modelling and Numerical Analysis, M2AN, Vol.38, no.4, pp.707-722, , 2004.
  • Tamaz Kaladze, Jemal Rogava, Luba Tsamalashvili, Mikheil Tsiklauri, On numerical resolution and uniqueness of solution of initial-boundary value problem for the generalized Charney-Obukhov equation, Reports of Enlarged Session of the Seminar of I.Vekua Institute of Applied Mathematics Vol. 19, N1, Tbilisi University Press, 2004.
  • Tamaz Kaladze, Jemal Rogava, Luba Tsamalashvili, Mikheil Tsiklauri, First- and second-order accurate implicit difference schemes for the Charney–Obukhov equation, Physics Letters A,Vol: 328, Issue: 1,Page: 51-64, Elsevier, 2004.
  • Jemal Rogava, Mikheil Tsiklauri, Zurab Gegechkori, High degree precision decomposition method for the evolution problem with an operator under a split form, Paris, M2AN, Vol.36, no.4, pp. 693-704, , 2002.