Name:     GIVI  BERIKELASHVILI

Affiliation:

Andrea  Razmadze Mathematical Institute

of I. Javakhishvili Tbilisi State University

6, Tamarashvili Str., Tbilisi 0179 

Georgia

E-mail: bergi@rmi.ge,

            berikela@yahoo.com

Research Areas:

Mathematical analysis of numerical methods;
In particular: finite-difference schemes for partial differential equations; 
convergence rate estimates in Sobolev spaces;
high accuracy schemes;
nonlocal boundary value problems

Personal Data:

Education and Scientific Degree:

Languages:

Georgian, Russian, English

Positions Held and Academic Experience:

Teaching  Experience:

Fellowships and Grants:

• Research Grant of the Georgian Academy of Sciences  # 1.11.97 (1997-1999);
  "Approximation methods in functional equations"
• Research Grant of the Georgian Academy of Sciences  # 1.12.00 (2000-2001);
  "Projective and finite difference methods"
• Research Grant of the Georgian Academy of Sciences  # 1.12.02 (2002-2003);
  "Projective-iterative and finite difference methods"
• Research Grant of the Georgian Academy of Sciences  # 1.12.04 (2004-2005);
  "Stability and convergence of projective and finite difference methods for singular
   integral equations and elliptic boundary value problems"
• Georgian National Science Foundation Grant  # GNSF/ST06/3-005 (2006-2008);
   "Characteristic problems for some classes of   nonlinear hyperbolic equations"
• Shota Rustaveli National  Science Foundation Grant  # FR/406/5-106/12 (2013-2016)
  "Consistent estimates of convergence in the method of corrections with higher order differences"

   

Participations in Conferences and other Scientific Forums:

• All-Union Seminar in Theory and Numerical Methods in Shells and Plate Theory ( Tbilisi, Georgia, 1984);   
  Difference schemes   for    a mixed boundary value problem of the static theory of elasticity in a rectangle 

• Conference on Numerical  Methods  (Miskolc, Hungary, 1986);
  Convergence of difference schemes for elliptic   equations with  solutions in  fractional-order Sobolev  spaces

• 5^th  Conference on Numerical Methods (Miskolc, Hungary, 1990);
  On the convergence of the difference solution of the first biharmonic boundary value   problem

• Second Congress of Mathematicians of Georgia (Tbilisi, Georgia, 1997)                                                                                

• Mini-symposiumTICMI (Tbilisi,Georgia,1999);
  On generalized solutions of non-local elliptic problems

• DEMPh-03 International symposium on differential equations and mathematical physics (Tbilisi, Georgia, 2003);
  On a nonlocal generalization of the Dirichlet problem

• Int. School in Phys. and Math. (ISPM),  "Function Spaces, Integral Transforms and Applications in PDE" (Tbilisi, Georgia, 2005);
  On the existence of positive and oscillation solutions of differential equations with delayed arguments  

• 6^th  International Congress on Industrial and Applied Mathematics (ICIAM 07) (Zurich, Switzerland 2007);
  On the choice of initial conditions of difference schemes for parabolic equations

• Fourth Conference on Numerical Analysis and Applications (NAA' 08)(Lozenetz, Bulgaria, 2008);                                  
  Finite difference solution of a nonlinear Klein-Gordon equation with an external source

• Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics (Tbilisi, Georgia, 2008);
  Finite difference solution of a nonlinear Klein-Gordon equation with cubic nonlinearity

• International Conference on Modern Problems in Applied Mathematics, dedicated to the 90th Anniversary of the Iv. Javakhishvili Tbilisi State University & 40th Anniversary of the I. Vekua Institute of Applied Mathematics (Tbilisi 2008); 
  Difference method of solving the Darboux problem for nonlinear Klein-Gordon equation

• International Conference on Modern Problems in Applied Mathematics, dedicated to the 90^th Anniversary of the Iv. Javakhishvili Tbilisi State University & 40^th Anniversary of the I. Vekua Institute of Applied Mathematics  (Tbilisi 2008);  
  Finite difference shemes for one nonlocal biharmonic problem

• Conference of A.Razmadze Mathematical Institute, dedicated to  the 80-th birthday anniversary of Academician N.Berikashvili's, Tbilisi, Georgia, November 2-6, 2009;
  On a nonlocal generalization of the biharmonic Dirichlet problem

• 2^nd WSEAS International Conference on Finite differences, Finite elements, Finite volumes, Boundary elements. (Tbilisi 2009);
  Finite difference scheme for one mixed problem with integral condition

• Conference of A.Razmadze Mathematical Institute, dedicated to  the 120-th birthday anniversary of Academician N. Muskhelishvili, Tbilisi, Georgia, 29.11-3.12,  2010.
  Difference schemes for BBM equation

• International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2010) (19-25 September, 2010, Rhodes,  Greece);
  High order difference scheme for Helmholtz equation with mixed boundary conditions

• XXV Enlarged Sessions of the Seminar of  I. Vekua Institute of Applied Mathematics. April 21–23, 2011;
  On the convergence of difference schemes for generalized RLW  equation

• Second International Conference of the Georgian Mathematical Union (Batumi, Georgia 2011)
  Finite difference solution for MEW wave equation

• International Workshop on the Qualitative Theory of Differential Equations (QUALITDE-2011) Tbilisi, Georgia, 4-6 November, 2011.
  On the convergence of difference schemes for generalized BBM  equation

• III International Conference of the Georgian Mathematical Union (Batumi, Georgia 2012)
  On a numerical solution of one nonlocal boundary value problem with mixed Dirichlet-Neumann conditions

• XXVI Enlarged Sessions of the Seminar of  I. Vekua Institute of Applied Mathematics.  April 23–25, 2012 . 
  On the convergence of difference scheme approximating one nonlocal boundary value problem.

• IV International Conference of the Georgian Mathematical Union, 9-15 September, 2013.  
  The method of corrections with higher order differences for an elliptic equation with Dirichlet boundary conditions

• International Workshop on the Qualitative Theory of Differential Equations  "QUALITDE – 2013". December 20-22, 2013, Tbilisi, Georgia.
  Difference  schemes for one fully nonlocal boundary-value problem