Summary

Projects

• Development of analytical and numerical methods for calculating of cusped prismatic shells and beams (D-13/18), 2012-2014.
• Construction and Investigation of Hierarchical Mathematical Models for Medium Consisting of Deformable Solid and Fluid Parts (GNSF/ST06/3-035), 2006-2008.
• Planetary Waves and Nonlinear Solitary Vortical Structures in the Earth's Ionosphere (3317), 2003-2005.

Talks

• 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.
• 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.
• 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.
• 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.
• 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.
• 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

• 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.
• 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, 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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, 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.
• 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, 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.
• 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.
• 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.