• Board Member of the Georgian Union of Mathematicians
• Vice-president of Georgian Academy of Natural Sciences
• Georgian Society of History of Sciences
• President of the Georgian Scientists Association
• Board Member of the Accredit Council of the Higher Educational Institutions
• “Computational methods in applied mathematics”, Associate editor
• “Applied mathematics and Informatics”, Associate editor

During 35 years led various courses (basically at the TSU) in:

Information technologies of management, mathematics of finances, mathematical modelling, numerical methods, mathematical methods in economics.

Active part in implementation of the projects in:

1) A new approach to analizing fuzzy data supporting decision ­ making regarding the possibility of earthquake occurence (Project proposal #2126).

Project selected for funding in INTAS OPEN CALL 1997-200

Reference  # INTAS-97-2126.

2) Computer fund of Georgian Language.

Project selected for funding by Department of Sciences and Technology of Georgia 1989-1993

3) Statistical structures of Georgian Language.

Project selected for funding by Department of Sciences and Technology and Institute of Computing Mathematics of Georgian Academy of sciences 1994-1995.

4) The Numerical methods for solving nonlinear equations in partial derivatives and its application in synergetics. 1991-1995

The Academy of Sciences of Georgia.

5) Construction of algorithms for computing of two dimensianal gas dynamics problems in Euler variables. 1989-1991

The Academy of Sciences of Georgia

Supervised the work and defending of 11 Candidate dissertations

1) Computational methods in applied Mathematics, National Academy of Sciences, Minsk, Belarus, Associate Editor.

2) Applied Mathematics and Informatics, Tbilisi State University, Tbilisi

Associate Editor

1. H.Meladze, D.Potskishvili    On convergence of completely conservative Two-layer difference schemes of Gas-dynamics in Euler variables, Applied Mathematics and Informatics, vol. 1, #1, 1996, pp.111-118.

2. F.Criado, H. Meladze, N. Odishelidze    An Optimal Control Problem for Helmhooltz Equation with Non-local Boundary Conditions and Quadzatic Functional // Rev. R. Acad. Genc. Exact. Fis. Nat. (Esp) vol. 91, #1, 1997, 65-68

3. F.Criado, T.Gvelesiani, N.Jgamadze, H.Meladze    Two Mathematical Models for Investigating Wave Generation in Reservoizs // Applied Mathematics and Informatics, vol.2, 1997, 20-31

4. F.Criado, G.Gachechiladze, H.Meladze    Inverse Spline-interpolation for Numerical solving a piston problem with isothermic Gas Compression and constant velocity // International Journal of Computer Mathematics, vol.71, 1998, 83-95.

5. H.Meladze, N.Jgamadze, A.Chanturia, N.Skirtladze // Mathematical modelling of collapse of big volume mountainous Landslide masses // Geoecology and Computers, Balkema, Rotterdam ISBN 90/59090841, 2000, 199-202.

6. E.D.Gordeziani, H.Meladze, F.G.Torrabla // On Mathematical modelling and numerical resolution of pollution diffusion in river, Geology and Computers, Balkema, Rotterdam, ISBN 9058090841, 2000, 509-511.

7. H.Meladze, N.Odishelidze, F.Criado(J)    The Necessary Condition of the Optimality for an Optimal Control Problem for Helmholtz Equation with Non-local Boundary Conditions and a Non-linear Functional // Applied Mathematics and Informatics, vol. 4, #1, 1999, 66-74.

8. F.Criado, T.Davitashvili, N.Skhirtladze, H.Meladze    On one Numerical Method for solving some Self-Similarity problems of Gas-Dynamics on a Multiprocessor //Intern. J. Comput. Math., vol.74, #1, 2000, 63-85.

9. T.Davitashvili, T.Elizarova, F.Criado, H.Meladze, N.Skhirtladze    On Convergence of Cinatically – Coordinated Difference schemes of Gas-Dynamics, Preprint, Moscow, MSU, 1999, 1-35.

10. Meladze H.V., Skhirtladze N. M    Foundation of Applied Mathemetics , Manual for the University students, Tbilisi University Press, Tbilisi, 2000.

11. T. Davitashvili, T. Elizarova, F. Criado, G. Meladze, N. Skhirtladze     On Convergence of  Kinetically – Consistens Difference schemes of Gas-Dynamics // Mathematical  modelling, vol. 13, # 4,  Moscow, MSU, 2001,71-83.

• Numerical Methods.

• The direct and iteration methods of solution of problems of the linear algebra.

• The numerical schemes of gas and hydrodynamic problems.

• The different methods of solution of boundary value problems of mathematical physics.

•  Introduction to mathematical modeling

• The different methods of solution of problems of mathematical physics.

• Problems of the control theory for DE of elliptic type with non-local boundary conditions.

• The parallel iteration methods of solution of linear and nonlinear systems of algebraic equations for computers with multiprocessors (?)

• The mathematical models for problems of gas and hydro dynamics. The investigation of difference schemes for one and multi dimensional problems of gas and hydro dynamics.

• The economical (optimal) difference schemes for multidimensional problems of mathematical physics.

      The following dissertations have been completed under guidance of Prof. H.Meladze:

Ph.D.

1.  “The conditions of optimality and difference methods for solving the control theory problems for elliptic equations”
   Deradze D.Sh., Ph.D. (Mathematics), 1988, Institute of Computing Mathematics.

2.  “Iterative methods of decomposition for solving the systems with block-threediagonal matrix”.  
   Bliadze I.D., Ph.D. (Mathematics), 1989. Institute of Computing Mathematics.

3. “The questions of construction and investigation of mathematical models of super fluid phases  3He.”
    Mikeladze S.V.,Ph.D. (Mathematics), 1989. Institute of Computing Mathematics.

4.  “On construction of polynoms for chebishev iterative processes”. 
   Buhnikashvili I.A., Ph.D. (Mathematics), 1990. Institute of Computing  Mathematics.

5. “On convergence of difference schemes for two-dimensional equations of gas-dynamics in Euler variables”.
   Djgamadze N.O., Ph.D. (Mathematics), 1991. Institute of Computing Mathematics.

6. “The numericalmethods for solving the nonlinear equations in partial derivaires and its application in synergetic”.
   Tsertsvadze G.Z., Ph.D. (Mathematics), 1992. Institute of  Mathematical modeling of Russian Academy.

7. “The investigation of magnetohydrodynamic processes by self-semilary solution and numerical methods with nonlinear volume sources and sinks”.
   Edjibia G.V., Ph.D. (Mathematics), 1993. Institute of Computing Mathematics.

8.  “The method of characteristics for the classes of second order quasilinea equations in initial and inverse problems”.
   Menteshashvili M.Z., Ph.D. (Mathematics), 1995. Institute of Computing Mathematics.

9. “The Difference schemes for solution of optimal control problem for second order elliptic equations with non local boundary conditions”.
   Odishelidze N.T., Ph.D. (Mathematics), 1995. Institute of Computing Mathematics.

10. “The parallel numerical methods of solution for hyperbolic equations and systems of equations, which simulate the problems of continuum mechanics”.
    Gachechiladze G.T., Ph.D. (Mathematics), 1995. Institute of Computing Mathematics.