Volume 38, Number 4, July-August 2004
|Page(s)||707 - 722|
|Published online||15 August 2004|
- V.B. Andreev, On difference schemes with a splitting operator for general p-dimensional parabolic equations of second order with mixed derivatives . SSSR Comput. Math. Math. Phys. 7 (1967) 312–321.
- G.A. Baker, An implicit, numerical method for solving the two-dimensional heat equation. Quart. Appl. Math. 17 (1959/1960) 440–443.
- G.A. Baker and T.A. Oliphant, An implicit, numerical method for solving the two-dimensional heat equation . Quart. Appl. Math. 17 (1959/1960) 361–373.
- G. Birkhoff and R.S. Varga, Implicit alternating direction methods . Trans. Amer. Math. Soc. 92 (1959) 13–24. [MathSciNet]
- G. Birkhoff, R.S. Varga and D. Young, Alternating direction implicit methods . Adv. Comput. Academic Press, New York 3 (1962) 189–273.
- P.R. Chernoff, Note on product formulas for operators semigroups . J. Functional Anal. 2 (1968) 238–242. [CrossRef]
- P.R. Chernoff, Semigroup product formulas and addition of unbounded operators . Bull. Amer. Mat. Soc. 76 (1970) 395–398. [CrossRef]
- B.O. Dia and M. Schatzman, Comutateurs semi-groupes holomorphes et applications aux directions alternées . RAIRO Modél. Math. Anal. Numér. 30 (1996) 343–383. [MathSciNet]
- E.G. Diakonov, Difference schemes with a splitting operator for nonstationary equations . Dokl. Akad. Nauk SSSR 144 (1962) 29–32. [MathSciNet]
- E.G. Diakonov, Difference schemes with splitting operator for higher-dimensional non-stationary problems . SSSR Comput. Math. Math. Phys. 2 (1962) 549–568.
- J. Douglas, On numerical integration of by impilicit methods . SIAM 9 (1955) 42–65.
- J. Douglas and H. Rachford, On the numerical solution of heat condition problems in two and three space variables . Trans. Amer. Math. Soc. 82 (1956) 421–439. [CrossRef] [MathSciNet]
- M. Dryja, Stability in W22 of schemes with splitting operators . SSSR. Comput. Math. Math. Phys. 7 (1967) 296–302.
- G. Fairweather, A.R. Gourlay and A.R. Mitchell, Some high accuracy difference schemes with a splitting operator for equations of parabolic and elliptic type . Numer. Math. 10 (1967) 56–66. [CrossRef] [MathSciNet]
- I.V. Fryazinov, Increased precision order economical schemes for the solution of parabolic type multi-dimensional equations . SSSR. Comput. Math. Math. Phys. 9 (1969) 1319–1326.
- Z.G. Gegechkori, J.L. Rogava and M.A. Tsiklauri, High-degree precision decomposition method for an evolution problem . Tbilisi, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics 14 (1999) 45–48.
- Z.G. Gegechkori, J.L. Rogava and M.A. Tsiklauri, High degree precision decomposition formulas of semigroup approximation . Tbilisi, Reports of Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics 16 (2001) 89–92.
- Z.G. Gegechkori, J.L. Rogava and M.A. Tsiklauri, Sequention-Parallel method of high degree precision for Cauchy abstract problem solution. Minsk, Comput. Methods in Appl. Math. 1 (2001) 173–187.
- Z.G. Gegechkori, J.L. Rogava and M.A. Tsiklauri, High degree precision decomposition method for the evolution problem with an operator under a split form . ESAIM: M2AN 36 (2002) 693–704. [CrossRef] [EDP Sciences]
- D.G. Gordeziani, On application of local one-dimensional method for solving parabolic type multi-dimensional problems of 2m-degree, Proc. of Science Academy of GSSR 3 (1965) 535–542.
- D.G. Gordeziani and A.A. Samarskii, Some problems of plates and shells thermo elasticity and method of summary approximation . Complex analysis and it's applications (1978) 173–186.
- D.G. Gordeziani and H.V. Meladze, On modeling multi-dimensional quasi-linear equation of parabolic type by one-dimensional ones, Proc. of Science Academy of GSSR 60 (1970) 537–540.
- D.G. Gordeziani and H.V. Meladze, On modeling of third boundary value problem for the multi-dimensional parabolic equations of arbitrary area by the one-dimensional equations . SSSR Comput. Math. Math. Phys. 14 (1974) 246–250. [CrossRef]
- A.R. Gourlay and A.R. Mitchell, Intermediate boundary corrections for split operator methods in three dimensions . Nordisk Tidskr. Informations-Behandling 7 (1967) 31–38. [MathSciNet]
- N.N. Ianenko, On Economic Implicit Schemes (Fractional steps method) . Dokl. Akad. Nauk SSSR 134 (1960) 84–86.
- N.N. Ianenko, Fractional steps method of solving for multi-dimensional problems of mathematical physics . Novosibirsk, Nauka (1967).
- N.N. Ianenko and G.V. Demidov, The method of weak approximation as a constructive method for building up a solution of the Cauchy problem . Izdat. “Nauka”, Sibirsk. Otdel., Novosibirsk. Certain Problems Numer. Appl. Math. (1966) 60–83.
- T. Ichinose and S. Takanobu, The norm estimate of the difference between the Kac operator and the Schrodinger emigroup . Nagoya Math. J. 149 (1998) 53–81. [MathSciNet]
- T. Ichinose and H. Tamura, The norm convergence of the Trotter-Kato product formula with error bound . Commun. Math. Phys. 217 (2001) 489–502. [CrossRef]
- V.P. Ilin, On the splitting of difference parabolic and elliptic equations . Sibirsk. Mat. Zh 6 (1965) 1425–1428.
- K. Iosida, Functional analysis . Springer-Verlag (1965).
- T. Kato, The theory of perturbations of linear operators . Mir (1972).
- A.N. Konovalov, The fractional step method for solving the Cauchy problem for an n-dimensional oscillation equation . Dokl. Akad. Nauk SSSR 147 (1962) 25–27. [MathSciNet]
- S.G. Krein, Linear equations in Banach space . Nauka (1971).
- A.M. Kuzyk and V.L. Makarov, Estimation of an exactitude of summarized approximation of a solution of Cauchy abstract problem . Dokl. Akad. Nauk USSR 275 (1984) 297–301.
- G.I. Marchuk, Split methods . Nauka (1988).
- G.I. Marchuk and N.N. Ianenko, The solution of a multi-dimensional kinetic equation by the splitting method . Dokl. Akad. Nauk SSSR 157 (1964) 1291–1292. [MathSciNet]
- G.I. Marchuk and U.M. Sultangazin, On a proof of the splitting method for the equation of radiation transfer . SSSR. Comput. Math. Math. Phys. 5 (1965) 852–863.
- D. Peaceman and H. Rachford, The numerical solution of parabolic and elliptic differential equations . SIAM 3 (1955) 28–41.
- M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness . New York-London, Academic Press [Harcourt Brace Jovanovich, Publishers] (1975).
- J.L. Rogava, On the error estimation of Trotter type formulas in the case of self-Andjoint operator . Functional analysis and its aplication 27 (1993) 84–86.
- J.L. Rogava, Semi-discrete schemes for operator differential equations . Tbilisi, Georgian Technical University press (1995).
- A.A. Samarskii, On an economical difference method for the solution of a multi-dimensional parabolic equation in an arbitrary region . SSSR Comput. Math. Math. Phys. 2 (1962) 787–811.
- A.A. Samarskii, On the convergence of the method of fractional steps for the heat equation . SSSR Comput. Math. Math. Phys. 2 (1962) 1117–1121.
- A.A. Samarskii, Locally homogeneous difference schemes for higher-dimensional equations of hyperbolic type in an arbitrary region. SSSR Comput. Math. Math. Phys. 4 (1962) 638–648.
- A.A. Samarskii, P.N. Vabishchevich, Additive schemes for mathematical physics problems . Nauka (1999).
- Q. Sheng, Solving linear partial differential equation by exponential spliting . IMA J. Numerical Anal. 9 (1989) 199–212. [CrossRef] [MathSciNet]
- R. Temam, Sur la stabilité et la convergence de la méthode des pas fractionnaires . Ann. Mat. Pura Appl. 4 (1968) 191–379.
- H. Trotter, On the product of semigroup of operators . Proc. Amer. Mat. Soc. 10 (1959) 545–551. [CrossRef] [MathSciNet]
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