
Adam Dzhishkariani
(1930 
2005)

Personal Data:
Date of Birth: 
January 22, 1930 
Place of Birth: 
The village AkhaliKhibulai, 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 BubnovGalerkin, method of least
squares, the collocation methods, method of the finite elements, projectiveiterative methods)
List of Main Publications
 Some error estimates in the RitzGalerkin method for ordinary
differential equations. (Russian) Trudy Tbiliss.
Mat. Inst. Razmadze 26 (1959), 285306.
 Error
estimates in the Ritz method for a nonhomogeneous differential equation.
(Russian) Soobshch. Akad. Nauk Gruzin. SSR 25 (1960),
257262.
 Error estimates in the Ritz method for eigenvalues and
eigenfunctions of a differential equation. (Russian) Soobshch. Akad.
Nauk Gruzin. SSR 25 (1960), 1118.
 On the rate of
convergence of the Ritz method for eigenvalues of differential operators.
(Russian) Soobshch. Akad. Nauk Gruzin. SSR 28 (1962),
513519.
 On the rate of convergence of Ritz's approximate method. (Russian)
Zh. Vychislit. Mat. Mat. Fiz. 3(1963), 654663;
English. transl.: USSR Comput. Math. Math. Phys. 3(1963), 879891.
 On the convergence speed of BubnovGalerkin method. (Russian)
Zh. vychisl. Mat. Mat. Fiz. 4(1964), No. 2, 343348.
 On the rapidity of convergence of the method of least squares. (Russian)
Trudy Tbiliss. Mat. Inst. Razmadze
29 (1964), 213217 (1964).
 The rapidity of convergence of
generalized Ritz and BubnovGalerkin methods. (Russian) Soobshch. Akad.
Nauk Gruzin. SSR 46 (1967), 553560.
 The
BubnovGalerkin method. (Russian) Zh. Vychisl. Mat. i Mat. Fiz.
7 (1967), 13981402.
 On the methods of Ritz and
BubnovGalerkin. (Russian) Soobshch. Akad. Nauk Gruzin. SSR
45 (1967), 1116.
 The Ritz method for a certain nonlinear equation.
(Russian) Soobshch. Akad. Nauk Gruzin. SSR 51 (1968),
1924.
 The least square and BubnovGalerkin methods. (Russian) Zh.
Vychisl. Mat. i Mat. Fiz. 8 (1968), 11101116.
 Some
remarks on direct methods. (Russian)
Trudy Tbiliss. Mat. Inst. Razmadze 36 (1969), 4756 (1970).
 The Ritz
approximation method for a certain nonlinear equation. (Russian)
Trudy Tbiliss. Mat. Inst. Razmadze 36 (1969),
2946 (1970).
 Certain remarks on direct methods. (Russian) Soobshch.
Akad. Nauk Gruzin. SSR 54 (1969), 541544.

Stability of the Ritz method for a certain nonlinear equation. (Russian)
Zh. Vychisl. Mat. i Mat. Fiz. 10 (1970), 840847.
 On
the question of the stability of approximate methods of variational type.
(Russian) Zh. Vychisl. Mat. i Mat. Fiz. 11 (1971),
569579.
 Some remarks on the general theory of approximate methods.
(Russian) Soobshch. Akad. Nauk Gruzin. SSR 69
(1973), 273275.
 The convergence of the BubnovGalerkin method for a
certain type of a nonlinear operator equation. (Russian) Zh. Vychisl.
Mat. i Mat. Fiz. 13 (1973), 459464, 533.
 On the
question of the stability of the GalerkinPetrov method. (Russian) A
collection of articles on the equations of mathematical physics. 4. Trudy Tbiliss. Mat. Inst. Razmadze 44
(1974), 5766.
 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), 6771.
 The stability and
convergence of approximate projection methods. (Russian) Collection of
articles on functional analysis, 2. Trudy Tbiliss.
Mat. Inst. Razmadze 50 (1975), 2233.
 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), 521.
 The solution of singular integral equations by approximate projection methods.
(Russian) Zh. Vychisl. Mat. Mat. Fiz. 19(1979), 11491161;
English transl.: USSR Comput. Math. Math. Phys. 19(1980),
No. 5, 6174.
 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), 3850.
 On the convergence of the residual in the finite element method. (Russian)
Dokl. Akad. Nauk SSSR 254(1980), 10521054; English transl.:
Sov. Math. Dokl. 22(1980), 503506.
 The solution of singular integral equations by collocation methods. (Russian)
Zh. Vychisl. Mat. Mat. Fiz. 21(1981), 355362; English transl.:
USSR Comput. Math. Math. Phys. 21(1981), No. 2, 99107.
 Approximate solution of equations of the second kind. (Russian) Mat.
Zametki 32 (1982), No. 4, 511516, 590; English transl.:
Math. Notes 32 (1983), 735738.
 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), 5667.
 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), 4656.
 On the approximate solution of a class of singular integral equations.
(Russian) Trudy Tbiliss. Mat. Inst. Razmadze
81 (1986), 4149.
 Superconvergence of an approximate projection method
with one iteration. (Russian) Current problems in mathematical physics,
Vol. I (Russian) (Tbilisi, 1987), 231238, 483, Tbilis. Gos.
Univ., Tbilisi, 1987.
 On the convergence of the finite element
method with one iteration. (Russian) Zh. Vychisl. Mat. i Mat. Fiz.
30 (1990), no. 5, 791796, 800; translation in USSR Comput. Math. Math. Phys. 30 (1990), no. 3,
112116 (1991).
 On the method of finite elements with one iteration.
Numerical methods (Miskolc, 1990), 165171, Colloq. Math. Soc. János
Bolyai, 59, NorthHolland, Amsterdam, 1991.
 On the
superconvergence of an approximate projection method with one iteration
(with G. S. Manveliani). (Russian)
Proc. A. Razmadze Math. Inst. 100 (1992), 8995.
 On the
approximate solutions of a class of singular integral equations.
Continuum mechanics and related problems of analysis (Tbilisi, 1991),
235239, "Metsniereba", Tbilisi, 1993.
 The order of congruence of
projectioniteration method (with A. Svanidze). (Russian) Reports of Enlarged Session of
Seminar of I. Vekua Inst. Appl. Math. 10 (1995), No. 3, 1619.
 On projective method of approximate
solution of singular integral equations (with G. Khvedelidze). Georgian Math. J.
3 (1996), No. 5, 457474.
 The convergence rate of an iterative projection method. (Russian) Zh. Vychisl.
Mat. Mat. Fiz. 37 (1997), No. 6, 663669; English transl.:
Comput. Math. Math. Phys. 37 (1997), No. 6, 646652.
 Projectiveiterative method of solution of integral equations
(with G. Khvedelidze). Proc. A. Razmadze Math. Inst. 120(1999), 2747.
 Stability of projectioniterative methods. (Russian) Zh. Vychisl. Mat. Mat.
Phys. 39(1999), No. 7, 10741084; English transl.:
Comput. Math. Math. Phys. 39(1999), No. 7, 10341044.
 On the residual convergence in projection and projectiveiterative methods
(with A. Svanidze). Proc. A. Razmadze Math. Inst. 124(2000), 3154.
 On projectioniteration method (with G. Khvedelidze).
Reports of Enlarged Session of Seminar of I. Vekua Inst. Appl. Math.
26 (2000), 314.
 On version of GalerkinPetrov's method
with iterations (with A. Svanidze). Proc. A. Razmadze Math. Inst.
132(2003), 7187.
 Method of GalerkinPetrov. (Russian) J. Vichisl. Mat.
i Mat. Fiz., 2003, No. 3, 7187.