List of Main Publications of Givi Berikelashvili

  1. On a difference scheme of high-order accuracy for elliptic systems. (Russian) Soobshch. Akad. Nauk Gruz. SSR 71(1973), No. 2, 285-288.

  2. Two-layer schemes of high-order accuracy for systems of parabolic equations. (Russian) Soobshch. Akad. Nauk Gruz. SSR 72(1973), No. 1, 25-28.

  3. Triple-layer economical difference schemes of increased order of accuracy for hyperbolic system. (Russian) Soobshch. Akad. Nauk Gruz. SSR 72(1973), No. 2, 289-292.

  4. Three-level economical difference schemes of high-order accuracy for parabolic systems. (Russian) Soobshch. Akad. Nauk Gruz. SSR 74(1974), No. 3, 553-556.

  5. A scheme of higher-order accuracy for the solution of the third boundary value problem for the equation in a p-dimensional parallelepiped. (Russian) Soobshch. Akad. Nauk Gruz. SSR 86(1977), No. 2, 281-284.

  6. A two-layer scheme of higher order accuracy for solving the third boundary value problem of a p-dimensional heat equation. (Russian) Soobshch. Akad. Nauk Gruz. SSR 89(1978), No. 2, 297-300.

  7. A high-order accuracy difference scheme of Dirichlet problem for the Laplace equation with discountinuous boundary conditions. (Russian) Soobshch. Akad. Nauk Gruz. SSR 92(1978), No. 1, 29-32.

  8. Uniformly convergent three-layer difference schemes of higher-order accuracy for a multi-dimensional heat equation. (Russian) Soobshch. Akad. Nauk Gruz. SSR 92(1978), No. 2, 285-288.

  9. On one approach to the difference method of solving the bending problem of orthotropic plates. (Russian) Soobshch. Akad. Nauk Gruz. SSR 96(1979), No. 2, 281-284.

  10. On the approximate solution of some systems of nonlinear Volterra integral equations of the second kind (with G. D. Pavlenishvili). (Russian) Soobshch. Akad. Nauk Gruz. SSR 99(1980), No. 2, 313-316.

  11. Difference schemes for a mixed boundary value problem of the static theory of elasticity in a rectangle. (Russian) Theory and numerical methods of calculating plates and shells, Vol. II, Tbilis. Gos. Univ., Tbilisi, 1984, 33-36.

  12. On the order of convergence of difference schemes for an elliptic equation with mixed boundary conditions. (Russian) Soobshch. Akad. Nauk Gruz. SSR 118(1985), No. 2, 285-288.

  13. About the question on accuracy estimates of the Richardson extrapolation method for strongly elliptic systems. (Russian) Soobshch. Akad. Nauk Gruz. SSR 118(1985), No. 1, 45-48.

  14. The difference scheme of higher order accuracy for a heat equation in a rectangle (with M. N. Moskal'kov). (Russian) Ukr. NIINTI 30.07.85, No. 1607-Uk., Kiev, 1985, p. 16.

  15. On the convergence of the difference schemes for elliptic equations with variable coefficients and solutions from Sobolev spaces (with G. I. Sulkhanishvili). (Russian) Gruz. NIINTI 04.12.85, No. 190-G., Tbilisi, 1985, p. 16.

  16.  On a difference scheme of high accuracy for an elliptic equation with mixed derivative.   (Russian) Gruz. NIINTI 01.10.1986, No. 250-G, Tbilisi, 1986, p.8.

  17.  Convergence of some difference schemes of high accuracy for an elliptic systems without   mixed derivatives. (Russian) Gruz. NIINTI 01.10.1986, No. 251-G, Tbilisi, 1986, p.10.

  18. On the order of convergence of difference schemes for elliptic systems with solutions from Sobolev spaces (with G. I. Sulkhanishvili). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 87(1987), 21-28.

  19. To the of solving a discharge circuit equation of an electrical-hydraulic power transformer (with I. Nakashidze, D. Vardzelashvili, and A. Sikharulidze). (Russian) Electrical power processes and plants., Tbilisi, 1987, 85-88; Transact. of Georgian Polytechnic Institute 3(315).

  20. Convergence of some difference schemes for elliptic equations with variable coefficients. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 90(1988), 16-24.

  21. Schemes of high accuracy for an elliptic equation with mixed derivative (with V. G. Prikazchikov). (Russian) Differentsial'nye Uravneniya 25(1989), No. 9, 1622-1624.

  22. The convergence in W22 of a difference solution of the Dirichlet problem. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 30(1990), No. 3, 470-474; English transl.: USSR Comput. Math. Math. Phys. 30(1990), No. 2, 89-92.

  23. On the convergence of the difference solution of the first biharmonic boundary value problem (with M. G. Mirianashvili). Numerical methods, Proc. Conf., Miskolc/Hungary, 1990, Colloq. Math. Soc. Janos Bolyai 59(1991), 133-143.

  24. On the application of the net method to the solution of one class of problems of the theory of optimal control (with D. Devadze). (Russian) Current problems of applied mathematics and cybernetics, Tbilisi University Press, 1991, 53-56.

  25. On the convergence of Richardson's extrapolation method for elliptic equations. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 96(1991), 3-14.

  26. On the convergence in W21 of difference solutions for an elliptic equation with mixed boundary conditions (with M. D. Chkhartishvili ). (Russian) Bull. Georgian Acad. Sci. 148(1993), No. 2, 180-184.

  27. On the convergence of the difference schemes on W21 for one mixed boundary value problem of theory of elasticity (with M. Chkhartishvili). Bull. Georgian Acad. Sci. 153(1996), No. 2, 195-198.

  28. On the rate of convergence of the difference solution of the bending problem of the orthotropic plates. Proc. A. Razmadze Math. Inst. 118(1998), 21-32.

  29. The convergence of the difference solution to the third boundary value problem of elasticity theory.(Russian) Zh. Vychisl. Mat. Mat. Fiz. 38(1998), No. 2, 310-314; English transl.: Comput. Math. Math. Phys. 38(1998), No. 2, 300-304.

  30. The difference shemes of high order accuracy for elliptic equations with lower derivatives. Proc. A. Razmadze Math. Inst. 117(1998), 1-6.

  31. On the definition of a nonlocal trace of a function. Reports of Enlarged Session of the Seminar of I. N. Vekua Inst. Appl. Math. 13(1998), No. 2, 2-5.

  32. The convergence in W21 of the difference solution to the third boundary value problem of elasticity theory. Reports of Enlarged Session of the Seminar of I. N. Vekua Inst. Appl. Math. 14(1999), No. 3, 24-26.

  33. On the solvability of a nonlocal boundary value problem in the weighted Sobolev spaces. Proc. A. Razmadze Math. Inst. 119(1999), 3-11.

  34. The convergence rate of a finite-difference solution of the first boundary value problem for a fourth-order elliptic equation. (Russian) Differentsial'nye Uravneniya 35(1999), No. 7, 958-963; English transl.: Differ. Equations 35(1999), No. 7, 967-973.

  35. Finite difference schemes for elliptic equations with mixed boundary conditions. Proc. A. Razmadze Math. Inst. 122(2000), 21-31.

  36. Finite difference schemes for some mixed boundary value problems. Proc. A. Razmadze Math. Inst. 127(2001), 77-87.

  37. On convergence of difference schemes for the third boundary value problem of elasticity theory. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 41(2001), No. 8, 1242-1249; English transl.: Comput. Math. Math. Phys. 41(2001), No. 8, 1182-1189.

  38. On the convergence of finite difference scheme for one nonlocal elliptic boundary value problem. Publ. Inst. Math. (Belgrad) 70(84)(2001).

  39. On a nonlocal boundary value problem for a two-dimensional elliptic equation. Comput. Methods Appl. Math. 3 (2003), No. 1, 35-44.

  40. On the rate of convergence of the difference solution of a nonlocal boundary value problem for a second-order elliptic equation. (Russian) Differentsial'nye Uravneniya 39 (2003), No. 7, 896-903, 1004-1005; English transl.: Differ. Equations 39 (2003), No. 7, 945-953

  41. To a nonlocal generalization of the Dirichlet problem. J. Inequal. Appl. V. 2006 (2006),    Article 93858. P. 1-6.

  42. On improved approximate solution on the Fredholm integral equation (with G. Karkarashvili).    Comput. Methods Appl. Math. 6 (2006) No.3, P. 264-268.

  43. Construction and analysis of difference schemes for some elliptic problems, and consistent    estimates of the rate of convergence. Mem. Differential Equations Math. Phys. 38 (2006),  1-131.

  44. Convergence of fourth order compact difference schemes for three-dimensional convection- diffusion equations (with M.M. Gupta and  M. Mirianashvili). SIAM J. Numer. Anal. 45 (2007), Issue 1. P. 443-456

  45. On one approach of investigation of asymptotic properties of solution of ordinary  differential equations with delay (with O.M. Dzhokhadze and R.G. Koplatadze).  Differentsial'nye Uravneniya 44(2008), no. 1, 19-38; English transl.: Differ. Equations 44(2008), no. 1, 19-39.

  46. On existence and absence of global solutions of the first Darboux problem for nonlinear   wave equations (with O.M. Dzhokhadze, B.G. Midodashvili and S.S. Kharibegashvili). Differentsial'nye Uravneniya 44(2008), no. 3, 359-372; English transl.: Differ. Equations 44(2008), no. 3, 374-389.

  47. On a three level difference scheme for the regularized long wave equation (with M. Mirianashvili).  Mem. Differential Equations Math. Phys. 46 (2009), 147-155.

  48. Finite-difference method of solving the darboux problem for the nonlinear Klein-Gordon equation (with O. Jokhadze, S. Kharibegashvili, and B. Midodashvili). Mem. Differential Equations Math. Phys. 47 (2009), 123-132.

  49. On a nonlocal generalization of the biharmonic Dirichlet problem (with D.G. Gordeziani). Differential Equations,  46 (2010), no. 3, 321-328.

  50. High order difference scheme for Helmholtz equation with mixed boundary conditions (with M. M. Gupta and M. Mirianashvili). ICNAAM 2010. AIP Conference Proceedings, 1281 (2010), 757-760.

  51. Finite difference solution of a nonlinear Klein-Gordon equation with an external source (witrh O. Jokhadze, S. Kharibegashvili and B. Midodashvili). Mathematics of Computation. 80 (2011), 847-862. 

  52. On the choice of initial conditions of difference schemes for parabolic equations (with M.M.Gupta and M.Mirianashvili). Mem. Differential Equations Math. Phys. 53 (2011), 29-38.

  53. Finite difference schemes for Benjamin-Bona-Mahony equation (with M. Mirianashvili). Proc. A. Razmadze Math. Inst. 155 (2011), 95-97.

  54. Finite difference solution of a MRLW equation (with L. Karalashvili and G. Chikadze). Proc. A. Razmadze Math. Inst. 156 (2011), 17-35

  55. A one-parameter family of difference schemes for the regularized long-wave equation (with M. Mirianashvili). Georgian Math. J. 18 (2011), no.4, 639-667.

  56. On the convergence of difference schemes for one nonlocal boundary value problem (with N. Khomeriki). Lith. Math, J., 52 (2012), no.  4, 353-362.

  57. On the fourth-order accurate difference scheme for Poisson's equation with nonlocal condition. Proc. A. Razmadze Math. Inst. 159 (2012),  134-137.

  58. On a weak solution of one nonlocal boundary-value problem. Proc. A. Razmadze Math. Inst. 162 (2013), 116-120.

  59. On a numerical solution of one nonlocal boundary-value problem with mixed Dirichlet-Neumann conditions (with N. Khomeriki). Lith. Math. J. 53 (2013), no.4, 367--380.

  60. On the convergence of difference schemes for generalized Benjamin-Bona-Mahony equation (with M. Mirianashvili). Numer. Methods Partial Differ. Eq. .30 (2014), no. 1, 301--320.

  61. Difference schemes for one fully nonlocal boundary-value problem (with N. Khomeriki). Nonlinear Analysis: Modelling and Control,  19 (2014), no.3 (submitted)

  62. Consistent estimates of convergence in the method of corrections with higher order differences (with B. Midodashvili). Differentsial'nye Uravneniya (submitted).