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Zh. Vychisl. Mat. Mat. Fiz., 1995, Volume 35, Number 5, Pages 739–752 (Mi zvmmf2402)  

This article is cited in 31 scientific papers (total in 31 papers)

On the convergence, uniform with respect to the small parameter, of A. A. Samarskii's monotone scheme and its modifications

V. B. Andreev, I. A. Savin

Moscow

Full text: PDF file (3598 kB)
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English version:
Computational Mathematics and Mathematical Physics, 1995, 35:5, 581–591

Bibliographic databases:
UDC: 519.632
Received: 27.04.1994

Citation: V. B. Andreev, I. A. Savin, “On the convergence, uniform with respect to the small parameter, of A. A. Samarskii's monotone scheme and its modifications”, Zh. Vychisl. Mat. Mat. Fiz., 35:5 (1995), 739–752; Comput. Math. Math. Phys., 35:5 (1995), 581–591

Citation in format AMSBIB
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\by V.~B.~Andreev, I.~A.~Savin
\paper On the convergence, uniform with respect to the small parameter, of A.\,A.~Samarskii's monotone scheme and its modifications
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1995
\vol 35
\issue 5
\pages 739--752
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\transl
\jour Comput. Math. Math. Phys.
\yr 1995
\vol 35
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\pages 581--591
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    Erratum

    This publication is cited in the following articles:
    1. Kopteva N.V., “Uniform convergence with respect to a small parameter of a four-point scheme for the one-dimensional stationary convection-diffusion equation”, Differ Equ, 32:7 (1996), 958–964  mathnet  mathscinet  zmath  isi
    2. V. B. Andreev, I. A. Savin, “The computation of boundary flow with uniform accuracy with respect to a small parameter”, Comput. Math. Math. Phys., 36:12 (1996), 1687–1692  mathnet  mathscinet  zmath  isi
    3. V. B. Andreev, N. V. Kopteva, “A study of difference schemes with the first derivative approximated by a central difference ratio”, Comput. Math. Math. Phys., 36:8 (1996), 1065–1078  mathnet  mathscinet  zmath  isi
    4. N. V. Kopteva, “On the uniform in small parameter convergence of a weighted scheme for the one-dimensional time-dependent convection–diffusion equation”, Comput. Math. Math. Phys., 37:10 (1997), 1173–1180  mathnet  mathscinet  zmath
    5. Andreev V.B., Kopteva N.V., “On the convergence, uniform with respect to a small parameter, of monotone three-point finite-difference approximations”, Differ Equ, 34:7 (1998), 921–929  mathscinet  zmath  isi
    6. V. B. Andreev, “Convergence of a modified Samarskij's monotonic scheme on a smoothly condensing grid”, Comput. Math. Math. Phys., 38:8 (1998), 1212–1224  mathnet  mathscinet  zmath
    7. N. V. Kopteva, “Uniform convergence with respect to a small parameter of a scheme with central difference on refining grids”, Comput. Math. Math. Phys., 39:10 (1999), 1594–1610  mathnet  mathscinet  zmath
    8. I. A. Brayanov, L. G. Volkov, “Uniform in a small parameter convergence of Samarskii's monotone scheme and its modification for the convection-diffusion equation with a concentrated source”, Comput. Math. Math. Phys., 40:4 (2000), 534–550  mathnet  mathscinet  zmath
    9. Andreev V.B., Kopteva N.V., “Uniform with respect to a small parameter convergence of difference schemes for a convection-diffusion problem”, Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems, 2000, 133–139  mathscinet  isi
    10. Kopteva N., Linss T., “Uniform second-order pointwise convergence of a central difference approximation for a quasilinear convection-diffusion problem”, J Comput Appl Math, 137:2 (2001), 257–267  crossref  mathscinet  zmath  isi
    11. Linss T., “Sufficient conditions for uniform convergence on layer-adapted grids”, Appl Numer Math, 37:1–2 (2001), 241–255  crossref  mathscinet  zmath  isi
    12. Linss T., “Uniform pointwise convergence of finite difference schemes using grid equidistribution”, Computing, 66:1 (2001), 27–39  crossref  mathscinet  zmath  isi
    13. V. B. Andreev, “Apriornye otsenki reshenii singulyarno vozmuschennykh dvukhtochechnykh kraevykh zadach”, Matem. modelirovanie, 14:5 (2002), 5–16  mathnet  mathscinet  zmath
    14. V. B. Andreev, “Anisotropic estimates of the Green function for a singularly perturbed two-dimensional monotone convection-diffusion equation operator and its applications”, Comput. Math. Math. Phys., 43:4 (2003), 521–528  mathnet  mathscinet  zmath
    15. V. G. Zverev, “On a special difference scheme for the solution of boundary value problems of heat and mass transfer”, Comput. Math. Math. Phys., 43:2 (2003), 255–267  mathnet  mathscinet  zmath
    16. Linss T., “Layer-adapted meshes for convection-diffusion problems”, Comput Methods Appl Mech Engrg, 192:9–10 (2003), 1061–1105  crossref  mathscinet  zmath  isi
    17. Brayanov I.A., “Uniformly convergent difference scheme for a singularly perturbed problem of mixed parabolic-elliptic type”, Numerical Analysis and its Applications, Lecture Notes in Computer Science, 3401, 2005, 211–218  crossref  zmath  isi
    18. Brayanov I.A., “Uniformly convergent finite volume difference scheme for 2D convection-dominated problem with discontinuous coefficients”, Applied Mathematics and Computation, 163:2 (2005), 645–665  crossref  mathscinet  zmath  isi
    19. Brayanov I.A., “Numerical solution of a two-dimensional singularly perturbed reaction-diffusion problem with discontinuous coefficients”, Applied Mathematics and Computation, 182:1 (2006), 631–643  crossref  mathscinet  zmath  isi
    20. Brayanov I.A., “Uniformly convergent difference scheme for singularly perturbed problem of mixed type”, Electron Trans Numer Anal, 23 (2006), 288–303  mathscinet  zmath  isi  elib
    21. Brayanov I.A., “Numerical solution of a mixed singularly perturbed parabolic-elliptic problem”, J Math Anal Appl, 320:1 (2006), 361–380  crossref  mathscinet  zmath  isi  elib
    22. Gracia J.L., O'Riordan E., “A defect-correction parameter-uniform numerical method for a singularly perturbed convection-diffusion problem in one dimension”, Numer Algorithms, 41:4 (2006), 359–385  crossref  mathscinet  zmath  isi  elib
    23. Teofanov L., Uzelac Z., “Family of quadratic spline difference schemes for a convection-diffusion problem”, Int J Comput Math, 84:1 (2007), 33–50  crossref  mathscinet  zmath  isi  elib
    24. Vulanovic R., “The layer-resolving transformation and mesh generation for quasilinear singular perturbation problems”, J Comput Appl Math, 203:1 (2007), 177–189  crossref  mathscinet  zmath  isi  elib
    25. Kopteva N., O'Riordan E., “Shishkin Meshes in the Numerical Solution of Singularly Perturbed Differential Equations”, Int J Numer Anal Model, 7:3 (2010), 393–415  mathscinet  zmath  isi  elib
    26. Linss T., “Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems Introduction”, Layer-Adapted Meshes for Reaction-Convection-Diffusion Problems, Lecture Notes in Mathematics, 1985, 2010, 1  crossref  mathscinet  isi
    27. A. I. Zadorin, S. V. Tikhovskaya, “Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme”, Num. Anal. Appl., 6:1 (2013), 9–23  mathnet  crossref  mathscinet  elib
    28. Sharma K.K., Rai P., Patidar K.C., “A Review on Singularly Perturbed Differential Equations with Turning Points and Interior Layers”, Appl. Math. Comput., 219:22 (2013), 10575–10609  crossref  mathscinet  zmath  isi  elib
    29. Vulanovic R., Teofanov L., “On the Quasilinear Boundary-Layer Problem and Its Numerical Solution”, J. Comput. Appl. Math., 268 (2014), 56–67  crossref  mathscinet  zmath  isi
    30. Tikhovskaya S.V., Zadorin A.I., “a Two-Grid Method With Richardson Extrapolation For a Semilinear Convection-Diffusion Problem”, Application of Mathematics in Technical and Natural Sciences (Amitans'15), AIP Conference Proceedings, 1684, ed. Todorov M., Amer Inst Physics, 2015, 090007  crossref  isi
    31. I. V. Popov, “O monotonnykh raznostnykh skhemakh”, Matem. modelirovanie, 31:8 (2019), 21–43  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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