Adam Dzhishkariani

(1930 - 2005)

 


Personal Data:

Date of Birth: January 22, 1930
Place of Birth: The village Akhali-Khibulai, Georgia
Nationality: Georgian
Marital Status: Married, three children

 

Education and Scientific Degree:

Graduated from the Faculty of Physics and Mathematics of Tbilisi State University in 1956 and then undertook postgraduate studies at the Leningrad Branch of the USSR Academy of Sciences Mathematical Institute, was awarded a Candidate of science degree in 1961 and subsequently obtained his Doctor of science degree in 1985.

 

Languages:

Georgian, Russian, German (partially)

 

Positions Held and Academic Experience:

He began his career as a Research Assistant at A. Razmadze Mathematical Institute of Georgian Academy of Sciences in 1959 was promoted to Senior Researcher of the same Institute in 1964 and is currently Head of the Researcher Section of Computational Mathematics of the same Institute and Lecturer at Tbilisi State University. He is a member of the Tbilisi Mathematical Society. He also is a reviewer of the journal "Mathematical Reviews".


Research Areas:

The approximate projective methods of the solution of the elliptic boundary value problems and of the singular integral equations (the methods of Ritz, of the Bubnov-Galerkin, method of least squares, the collocation methods, method of the finite elements, projective-iterative methods)

 

 

List of Main Publications

  1. Some error estimates in the Ritz-Galerkin method for ordinary differential equations. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 26 (1959), 285-306.
  2. Error estimates in the Ritz method for a non-homogeneous differential equation. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 25 (1960), 257-262.
  3. Error estimates in the Ritz method for eigenvalues and eigenfunctions of a differential equation. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 25 (1960), 11-18.
  4. On the rate of convergence of the Ritz method for eigenvalues of differential operators. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 28 (1962), 513-519.
  5. On the rate of convergence of Ritz's approximate method. (Russian) Zh. Vychislit. Mat. Mat. Fiz. 3(1963), 654-663; English. transl.: USSR Comput. Math. Math. Phys. 3(1963), 879-891.
  6. On the convergence speed of Bubnov-Galerkin method. (Russian) Zh. vychisl. Mat. Mat. Fiz. 4(1964), No. 2, 343-348.
  7. On the rapidity of convergence of the method of least squares. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 29 (1964), 213-217 (1964).
  8. The rapidity of convergence of generalized Ritz and Bubnov-Galerkin methods. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 46 (1967), 553-560.
  9. The Bubnov-Galerkin method. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 7 (1967), 1398-1402.
  10. On the methods of Ritz and Bubnov-Galerkin. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 45 (1967), 11-16.
  11. The Ritz method for a certain nonlinear equation. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 51 (1968), 19-24.
  12. The least square and Bubnov-Galerkin methods. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 8 (1968), 1110-1116.
  13. Some remarks on direct methods. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 36 (1969), 47-56 (1970).
  14. The Ritz approximation method for a certain nonlinear equation. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze  36 (1969), 29-46 (1970).
  15. Certain remarks on direct methods. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 54 (1969), 541-544.
  16. Stability of the Ritz method for a certain nonlinear equation. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 10 (1970), 840-847.
  17. On the question of the stability of approximate methods of variational type. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 11 (1971), 569-579.
  18. Some remarks on the general theory of approximate methods. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 69 (1973), 273-275.
  19. The convergence of the Bubnov-Galerkin method for a certain type of a nonlinear operator equation. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 13 (1973), 459-464, 533.
  20. On the question of the stability of the Galerkin-Petrov method. (Russian) A collection of articles on the equations of mathematical physics. 4. Trudy Tbiliss. Mat. Inst. Razmadze 44 (1974), 57-66.
  21. On the approximate solution of integral equations with a singular operator. (Russian) A collection of articles on the equations of mathematical physics. 4. Trudy Tbiliss. Mat. Inst. Razmadze 44 (1974), 67-71.
  22. The stability and convergence of approximate projection methods. (Russian) Collection of articles on functional analysis, 2. Trudy Tbiliss. Mat. Inst. Razmadze 50 (1975), 22-33.
  23. On the approximate solution of a certain type of a singular integral equation (with T. V. Gabedava). (Russian) Collection of articles on functional analysis, 2. Trudy Tbiliss. Mat. Inst. Razmadze 50 (1975), 5-21.
  24. The solution of singular integral equations by approximate projection methods. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 19(1979), 1149-1161; English transl.: USSR Comput. Math. Math. Phys. 19(1980), No. 5, 61-74.
  25. Similar difference operators. (Russian) Boundary properties of analytic functions, singular integral equations and some questions of harmonic analysis. Trudy Tbiliss. Mat. Inst. Razmadze 65 (1980), 38-50.
  26. On the convergence of the residual in the finite element method. (Russian) Dokl. Akad. Nauk SSSR 254(1980), 1052-1054; English transl.: Sov. Math. Dokl. 22(1980), 503-506.
  27. The solution of singular integral equations by collocation methods. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 21(1981), 355-362; English transl.: USSR Comput. Math. Math. Phys. 21(1981), No. 2, 99-107.
  28. Approximate solution of equations of the second kind. (Russian) Mat. Zametki 32 (1982), No. 4, 511-516, 590; English transl.: Math. Notes 32 (1983), 735-738.
  29. Numerical realization of a scheme for approximate solution of a singular integral equation (with A. I. Svanidze). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 71 (1982), 56-67.
  30. Approximate solution of certain singular integral equations of crack theory (with R. D. Bantsuri, T. V. Bochorishvili, and A. I. Svanidze). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 75 (1984), 46-56.
  31. On the approximate solution of a class of singular integral equations. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 81 (1986), 41-49.
  32. Superconvergence of an approximate projection method with one iteration. (Russian) Current problems in mathematical physics, Vol. I (Russian) (Tbilisi, 1987), 231-238, 483, Tbilis. Gos. Univ., Tbilisi, 1987.
  33. On the convergence of the finite element method with one iteration. (Russian) Zh. Vychisl. Mat. i Mat. Fiz. 30 (1990), no. 5, 791-796, 800; translation in USSR Comput. Math. Math. Phys. 30 (1990), no. 3, 112-116 (1991).
  34. On the method of finite elements with one iteration. Numerical methods (Miskolc, 1990), 165-171, Colloq. Math. Soc. János Bolyai, 59, North-Holland, Amsterdam, 1991.
  35. On the superconvergence of an approximate projection method with one iteration (with G. S. Manveliani). (Russian) Proc. A. Razmadze Math. Inst. 100 (1992), 89-95.
  36. On the approximate solutions of a class of singular integral equations. Continuum mechanics and related problems of analysis (Tbilisi, 1991), 235-239, "Metsniereba", Tbilisi, 1993.
  37. The order of congruence of projection-iteration method (with A. Svanidze). (Russian) Reports of Enlarged Session of Seminar of I. Vekua Inst. Appl. Math. 10 (1995), No. 3, 16-19.
  38. On projective method of approximate solution of singular integral equations (with G. Khvedelidze). Georgian Math. J. 3 (1996), No. 5, 457-474.
  39. The convergence rate of an iterative projection method. (Russian) Zh. Vychisl. Mat. Mat. Fiz. 37 (1997), No. 6, 663-669; English transl.: Comput. Math. Math. Phys. 37 (1997), No. 6, 646-652.
  40. Projective-iterative method of solution of integral equations (with G. Khvedelidze). Proc. A. Razmadze Math. Inst. 120(1999), 27-47.
  41. Stability of projection-iterative methods. (Russian) Zh. Vychisl. Mat. Mat. Phys. 39(1999), No. 7, 1074-1084; English transl.: Comput. Math. Math. Phys. 39(1999), No. 7, 1034-1044.
  42. On the residual convergence in projection and projective-iterative methods (with A. Svanidze). Proc. A. Razmadze Math. Inst. 124(2000), 31-54.
  43. On projection-iteration method (with G. Khvedelidze). Reports of Enlarged Session of Seminar of I. Vekua Inst. Appl. Math. 26 (2000), 3-14.
  44. On version of Galerkin-Petrov's method with iterations (with A. Svanidze). Proc. A. Razmadze Math. Inst. 132(2003), 71-87.
  45. Method of Galerkin-Petrov. (Russian) J. Vichisl. Mat. i Mat. Fiz., 2003, No. 3, 71-87.