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Uspekhi Mat. Nauk, 1973, Volume 28, Issue 2(170), Pages 121–182 (Mi umn4863)  

This article is cited in 25 scientific papers (total in 25 papers)

Iterative methods for elliptic difference equations

R. P. Fedorenko


Full text: PDF file (3181 kB)
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English version:
Russian Mathematical Surveys, 1973, 28:2, 129–195

Bibliographic databases:

UDC: 517.9
MSC: 39B12, 39A10, 35J25
Received: 14.12.1972

Citation: R. P. Fedorenko, “Iterative methods for elliptic difference equations”, Uspekhi Mat. Nauk, 28:2(170) (1973), 121–182; Russian Math. Surveys, 28:2 (1973), 129–195

Citation in format AMSBIB
\Bibitem{Fed73}
\by R.~P.~Fedorenko
\paper Iterative methods for elliptic difference equations
\jour Uspekhi Mat. Nauk
\yr 1973
\vol 28
\issue 2(170)
\pages 121--182
\mathnet{http://mi.mathnet.ru/umn4863}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=400733}
\zmath{https://zbmath.org/?q=an:0278.65105}
\transl
\jour Russian Math. Surveys
\yr 1973
\vol 28
\issue 2
\pages 129--195
\crossref{https://doi.org/10.1070/RM1973v028n02ABEH001542}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J.J. Monaghan, “Particle methods for hydrodynamics”, Computer Physics Reports, 3:2 (1985), 71  crossref
    2. A. Yu. Danilenko, “Solution of the Neumann problem for Poisson's equation by the multigrid method in the three-dimensional case”, U.S.S.R. Comput. Math. Math. Phys., 31:10 (1991), 74–80  mathnet  mathscinet  zmath  isi
    3. R. P. Fedorenko, “Some problems and approximate methods of computational mechanics”, Comput. Math. Math. Phys., 34:2 (1994), 223–241  mathnet  mathscinet  zmath  isi
    4. B. V. Pal'tsev, I. I. Chechel', “Real properties of bilinear finite element implementations of methods with the splitting of boundary conditions for a Stokes-type system”, Comput. Math. Math. Phys., 38:2 (1998), 238–251  mathnet  mathscinet  zmath
    5. A. S. Lozinskii, “Finite-element realization of iterative processes with splitting of boundary conditions for a Stokes-type system in nonconcentric annuli”, Comput. Math. Math. Phys., 41:8 (2001), 1145–1157  mathnet  mathscinet
    6. V. O. Belash, B. V. Pal'tsev, “Bicubic finite-element implementations of methods with splitting of boundary conditions for a Stokes-type system in a strip under the periodicity condition”, Comput. Math. Math. Phys., 42:2 (2002), 188–210  mathnet  mathscinet  zmath  elib
    7. B. V. Pal'tsev, I. I. Chechel', “Increasing the rate of convergence of bilinear finite-element realizations of iterative methods by splitting boundary conditions for Stokes-type systems for large values of a singular parameter”, Comput. Math. Math. Phys., 44:11 (2004), 1949–1967  mathnet  mathscinet  zmath
    8. B. V. Pal'tsev, I. I. Chechel', “Second-order accurate (up to the axis of symmetry) finite-element implementations of iterative methods with splitting of boundary conditions for Stokes and stokes-type systems in a spherical layer”, Comput. Math. Math. Phys., 45:5 (2005), 816–857  mathnet  mathscinet  zmath  elib
    9. B. V. Pal'tsev, I. I. Chechel', “Second-order accurate method with splitting of boundary conditions for solving the stationary axially symmetric Navier–Stokes problem in spherical gaps”, Comput. Math. Math. Phys., 45:12 (2005), 2148–2165  mathnet  mathscinet  zmath  elib
    10. B. V. Pal'tsev, I. I. Chechel', “On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers”, Comput. Math. Math. Phys., 46:5 (2006), 820–847  mathnet  crossref  mathscinet  elib  elib
    11. S. A. Gorbatkov, D. V. Polupanov, “Itero-approksimativnyi metod resheniya nelineinykh mnogomernykh zadach elektroteplovogo polya”, Matem. modelirovanie, 21:6 (2009), 110–120  mathnet  mathscinet  zmath
    12. V. T. Zhukov, “On explicit methods for the time integration of parabolic equations”, Math. Models Comput. Simul., 3:3 (2011), 311–332  mathnet  crossref  mathscinet
    13. M. B. Soloviev, “On numerical implementations of a new iterative method with boundary condition splitting for solving the nonstationary stokes problem in a strip with periodicity condition”, Comput. Math. Math. Phys., 50:10 (2010), 1682–1701  mathnet  crossref  adsnasa  isi  elib
    14. M. B. Soloviev, “Numerical implementations of an iterative method with boundary condition splitting as applied to the nonstationary stokes problem in the gap between coaxial cylinders”, Comput. Math. Math. Phys., 50:11 (2010), 1895–1913  mathnet  crossref  adsnasa  isi  elib
    15. A. V. Akhmetzyanov, A. M. Salnikov, S. V. Spiridonov, “Mnogosetochnye balansovye modeli nestatsionarnykh potokov v slozhnykh gazotransportnykh sistemakh”, UBS, 30.1 (2010), 230–251  mathnet  elib
    16. B. V. Pal'tsev, M. B. Soloviev, I. I. Chechel', “On the development of iterative methods with boundary condition splitting for solving boundary and initial-boundary value problems for the linearized and nonlinear Navier–Stokes equations”, Comput. Math. Math. Phys., 51:1 (2011), 68–87  mathnet  crossref  mathscinet  isi  elib
    17. Zhukov V.T., Novikova N.D., Feodoritova O.B., “Parallelnyi mnogosetochnyi metod dlya raznostnykh ellipticheskikh uravnenii. chast i. osnovnye elementy algoritma”, Preprinty IPM im. M.V. Keldysha, 2012, no. 30, 1–32  elib
    18. Zhukov V.T., Novikova N.D., Feodoritova O.B., “Parallelnyi mnogosetochnyi metod dlya raznostnykh ellipticheskikh uravnenii. anizotropnaya diffuziya”, Preprinty IPM im. M.V. Keldysha, 2012, no. 76, 1–36  elib
    19. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Parallelnyi mnogosetochnyi metod dlya raznostnykh ellipticheskikh uravnenii. \Chast I. Osnovnye elementy algoritma”, Preprinty IPM im. M. V. Keldysha, 2012, 030, 32 pp.  mathnet
    20. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Parallelnyi mnogosetochnyi metod dlya raznostnykh ellipticheskikh uravnenii. Anizotropnaya diffuziya”, Preprinty IPM im. M. V. Keldysha, 2012, 076, 36 pp.  mathnet
    21. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Parallel multigrid method for solving elliptic equations”, Math. Models Comput. Simul., 6:4 (2014), 425–434  mathnet  crossref
    22. M. B. Solov'ev, “Numerical implementation of an iterative method with boundary condition splitting for solving the nonstationary stokes problem on the basis of an asymptotically stable two-stage difference scheme”, Comput. Math. Math. Phys., 54:12 (2014), 1817–1825  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    23. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “Multigrid method for elliptic equations with anisotropic discontinuous coefficients”, Comput. Math. Math. Phys., 55:7 (2015), 1150–1163  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    24. V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “On the solution of evolution equations based on multigrid and explicit iterative methods”, Comput. Math. Math. Phys., 55:8 (2015), 1276–1289  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    25. T. P. Akishina, T. I. Grokhlina, P. V. Zrelov, V. V. Ivanov, R. V. Polozov, V. S. Sivozhelezov, V. A. Stepanenko, Yu. N. Chirgadze, A. V. Yakovlev, “Massovye vychisleniya elektrostaticheskikh potentsialov i kart molekulyarnykh poverkhnostei belkov i nukleinovykh kislot v raspredelennoi kompyuternoi srede: organizatsiya i algoritmy”, Matem. biologiya i bioinform., 12:2 (2017), 354–374  mathnet  crossref
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