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Zh. Vychisl. Mat. Mat. Fiz., 1984, Volume 24, Number 6, Pages 864–875 (Mi zvmmf4370)  

This article is cited in 19 scientific papers (total in 19 papers)

Increasing the accuracy of solutions of difference schemes for parabolic equations with a small parameter multiplying the highest derivative

G. I. Shishkin


Full text: PDF file (1296 kB)

English version:
USSR Computational Mathematics and Mathematical Physics, 1984, 24:3, 150–157

Bibliographic databases:

UDC: 519.633
MSC: Primary 65N12; Secondary 35K20
Received: 20.07.1982

Citation: G. I. Shishkin, “Increasing the accuracy of solutions of difference schemes for parabolic equations with a small parameter multiplying the highest derivative”, Zh. Vychisl. Mat. Mat. Fiz., 24:6 (1984), 864–875; U.S.S.R. Comput. Math. Math. Phys., 24:3 (1984), 150–157

Citation in format AMSBIB
\Bibitem{Shi84}
\by G.~I.~Shishkin
\paper Increasing the accuracy of solutions of difference schemes for parabolic equations with a~small parameter multiplying the highest derivative
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1984
\vol 24
\issue 6
\pages 864--875
\mathnet{http://mi.mathnet.ru/zvmmf4370}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=750096}
\zmath{https://zbmath.org/?q=an:0565.65057}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1984
\vol 24
\issue 3
\pages 150--157
\crossref{https://doi.org/10.1016/0041-5553(84)90063-6}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. I. Shishkin, “A grid approximation of the method of additive separation of singularities for a singularly perturbed equation of parabolic type”, Comput. Math. Math. Phys., 34:5 (1994), 621–637  mathnet  mathscinet  zmath  isi
    2. G. I. Shishkin, “Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations”, Comput. Math. Math. Phys., 35:4 (1995), 429–446  mathnet  mathscinet  zmath  isi
    3. I. A. Savin, “The rate of convergence on a piecewise-uniform grid of a difference scheme for the parabolic equation”, Comput. Math. Math. Phys., 36:11 (1996), 1573–1579  mathnet  mathscinet  zmath  isi
    4. G. I. Shishkin, “Grid approximation of parabolic equations with singular initial conditions”, Comput. Math. Math. Phys., 36:3 (1996), 341–356  mathnet  mathscinet  zmath  isi
    5. G. I. Shishkin, “Finite-difference approximations for singularly perturbed elliptic equations”, Comput. Math. Math. Phys., 38:12 (1998), 1909–1921  mathnet  mathscinet  zmath
    6. G. I. Shishkin, “An improved piecewise uniform mesh for a singularly perturbed elliptic reaction-diffusion equation”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 2, S138–S147  mathnet  mathscinet  zmath  elib
    7. Kopteva N., “Error expansion for an upwind scheme applied to a two-dimensional convection-diffusion problem”, SIAM J Numer Anal, 41:5 (2003), 1851–1869  crossref  mathscinet  zmath  isi
    8. P. W. Hemker, G. I. Shishkin, L. P. Shishkina, “High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation”, Comput. Math. Math. Phys., 44:2 (2004), 309–316  mathnet  mathscinet  zmath
    9. Shishkin G.I., Shishkina L.P., “A higher-order Richardson method for a quasilinear singularly perturbed elliptic reaction-diffusion equation”, Differ Equ, 41:7 (2005), 1030–1039  mathnet  crossref  mathscinet  zmath  isi  elib
    10. G. I. Shishkin, “Richardson's method for increasing the accuracy of difference solutions of singularly perturbed elliptic convection-diffusion equations”, Russian Math. (Iz. VUZ), 50:2 (2006), 57–71  mathnet  mathscinet  zmath
    11. G. I. Shishkin, “Metod povyshennoi tochnosti dlya kvazilineinogo singulyarno vozmuschennogo ellipticheskogo uravneniya konvektsii-diffuzii”, Sib. zhurn. vychisl. matem., 9:1 (2006), 81–108  mathnet  zmath
    12. G. I. Shishkin, “A method of asymptotic constructions of improved accuracy for a quasilinear singularly perturbed parabolic convection-diffusion equation”, Comput. Math. Math. Phys., 46:2 (2006), 231–250  mathnet  crossref  mathscinet  zmath
    13. Shishkin G.I., Shishkina L.P., “The Richardson extrapolation technique for quasilinear parabolic singularly perturbed convection-diffusion equations”, International Workshop on Multi-Rate Processes and Hysteresis, Journal of Physics Conference Series, 55, 2006, 203–213  crossref  isi
    14. G. I. Shishkin, “The Richardson scheme for the singularly perturbed parabolic reaction-diffusion equation in the case of a discontinuous initial condition”, Comput. Math. Math. Phys., 49:8 (2009), 1348–1368  mathnet  crossref  zmath  isi
    15. G. I. Shishkin, L. P. Shishkina, “A Richardson scheme of an increased order of accuracy for a semilinear singularly perturbed elliptic convection-diffusion equation”, Comput. Math. Math. Phys., 50:3 (2010), 437–456  mathnet  crossref  mathscinet  adsnasa  isi
    16. G. I. Shishkin, L. P. Shishkina, “A Richardson scheme of the decomposition method for solving singularly perturbed parabolic reaction-diffusion equation”, Comput. Math. Math. Phys., 50:12 (2010), 2003–2022  mathnet  crossref  adsnasa
    17. Kadalbajoo M.K., Gupta V., “A brief survey on numerical methods for solving singularly perturbed problems”, Applied Mathematics and Computation, 217:8 (2010), 3641–3716  crossref  mathscinet  zmath  isi
    18. 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
    19. Shishkin G.I., Shishkina L.P., “Iterative Newton solution method for the Richardson scheme for a semilinear singular perturbed elliptic convection-diffusion equation”, Russian J Numer Anal Math Modelling, 26:4 (2011), 427–445  crossref  mathscinet  zmath  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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