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Zh. Vychisl. Mat. Mat. Fiz., 1996, Volume 36, Number 8, Pages 101–117 (Mi zvmmf2202)  

This article is cited in 32 scientific papers (total in 32 papers)

A study of difference schemes with the first derivative approximated by a central difference ratio

V. B. Andreev, N. V. Kopteva

Moscow

Full text: PDF file (342 kB)
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English version:
Computational Mathematics and Mathematical Physics, 1996, 36:8, 1065–1078

Bibliographic databases:
UDC: 519.632
MSC: Primary 65L10; Secondary 65L12, 65L50, 65L70, 34B05, 34E15
Received: 28.04.1995

Citation: V. B. Andreev, N. V. Kopteva, “A study of difference schemes with the first derivative approximated by a central difference ratio”, Zh. Vychisl. Mat. Mat. Fiz., 36:8 (1996), 101–117; Comput. Math. Math. Phys., 36:8 (1996), 1065–1078

Citation in format AMSBIB
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\paper A study of difference schemes with the first derivative approximated by a central difference ratio
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1996
\vol 36
\issue 8
\pages 101--117
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\transl
\jour Comput. Math. Math. Phys.
\yr 1996
\vol 36
\issue 8
\pages 1065--1078
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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. 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. Stynes M., ORiordan E., “A uniformly convergent galerkin method on a Shishkin mesh for a convection-diffusion problem”, J Math Anal Appl, 214:1 (1997), 36–54  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. 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
    5. 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
    6. 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
    7. Linss T., “An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem”, J Comput Appl Math, 110:1 (1999), 93–104  crossref  mathscinet  zmath  isi  scopus
    8. Clavero C., Gracia J.L., Lisbona F., “High order methods on Shishkin meshes for singular perturbation problems of convection-diffusion type”, Numer Algorithms, 22:1 (1999), 73–97  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Lenferink W., “Pointwise convergence of approximations to a convection-diffusion equation on a Shishkin mesh”, Appl Numer Math, 32:1 (2000), 69–86  crossref  mathscinet  zmath  isi  scopus
    10. Linss T., “A novel Shishkin-type mesh for convection-diffusion problems”, Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems, 2000, 199–204  isi
    11. 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
    12. Roos H.G., Linss T., “Gradient recovery for singularly perturbed boundary value problems I: One-dimensional convection-diffusion”, Computing, 66:2 (2001), 163–178  crossref  mathscinet  zmath  isi  scopus
    13. Roos H.G., “On a stabilization effect of thin submeshes for convection-diffusion problems”, Zeitschrift fur Angewandte Mathematik und Mechanik, 81:9 (2001), 637–639  crossref  mathscinet  zmath  isi
    14. 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  adsnasa  isi  scopus
    15. Kopteva N., “Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem”, SIAM J Numer Anal, 39:2 (2001), 423–441  crossref  mathscinet  zmath  isi  scopus
    16. Linss T., “Sufficient conditions for uniform convergence on layer-adapted grids”, Appl Numer Math, 37:1–2 (2001), 241–255  crossref  mathscinet  zmath  isi  scopus
    17. Linss T., “Uniform pointwise convergence of finite difference schemes using grid equidistribution”, Computing, 66:1 (2001), 27–39  crossref  mathscinet  zmath  isi  scopus
    18. Vulanovic R., “A higher-order scheme for quasilinear boundary value problems with two small parameters”, Computing, 67:4 (2001), 287–303  crossref  mathscinet  zmath  isi  scopus
    19. Lenferink W., “A second order scheme for a time-dependent, singularly perturbed convection-diffusion equation”, J Comput Appl Math, 143:1 (2002), 49–68  crossref  mathscinet  zmath  adsnasa  isi  scopus
    20. Linss T., “Layer-adapted meshes for convection-diffusion problems”, Comput Methods Appl Mech Engrg, 192:9–10 (2003), 1061–1105  crossref  mathscinet  zmath  adsnasa  isi  scopus
    21. Clavero C., Gracia J.L., “HODIE finite difference schemes on generalized Shishkin meshes”, J Comput Appl Math, 164 (2004), 195–206  crossref  mathscinet  zmath  adsnasa  isi  scopus
    22. Portero L., Jorge J.C., “Special meshes and domain decomposition methods for evolutionary convection-diffusion-reaction problems”, International Journal For Numerical Methods in Fluids, 47:10–11 (2005), 1237–1243  crossref  mathscinet  zmath  adsnasa  isi  scopus
    23. 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  adsnasa  isi  elib  scopus
    24. Gracia J.L., O'Riordan E., Pickett M.L., “A parameter robust second order numerical method for a singularly perturbed two-parameter problem”, Appl Numer Math, 56:7 (2006), 962–980  crossref  mathscinet  zmath  isi  scopus
    25. 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  scopus
    26. 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
    27. 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  adsnasa  isi
    28. 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  scopus
    29. Gracia J.L., O'Riordan E., “Scaled Discrete Derivatives of Singularly Perturbed Elliptic Problems”, Numer. Meth. Part Differ. Equ., 31:1 (2015), 225–252  crossref  mathscinet  zmath  isi  elib  scopus
    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  scopus
    31. Sharma M., “A Robust Numerical Approach For Singularly Perturbed Time Delayed Parabolic Partial Differential Equations”, Differ. Equat. Dyn. Syst., 25:2, SI (2017), 287–300  crossref  mathscinet  zmath  isi  scopus
    32. Echeverria C., Liesen J., Szyld D.B., Tichy P., “Convergence of the Multiplicative Schwarz Method For Singularly Perturbed Convection-Diffusion Problems Discretized on a Shishkin Mesh”, Electron. Trans. Numer. Anal., 48 (2018), 40–62  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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