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Zh. Vychisl. Mat. Mat. Fiz., 2004, Volume 44, Number 2, Pages 329–337 (Mi zvmmf896)  

This article is cited in 14 scientific papers (total in 14 papers)

High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation

P. W. Hemkera, G. I. Shishkinb, L. P. Shishkinab

a Centrum voor Wiskunde en Informatica, Amsterdam
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

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English version:
Computational Mathematics and Mathematical Physics, 2004, 44:2, 309–316

Bibliographic databases:
UDC: 519.632.4
MSC: Primary 65N06; Secondary 35B25, 35J25, 65N15, 65N55
Received: 29.08.2002

Citation: 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”, Zh. Vychisl. Mat. Mat. Fiz., 44:2 (2004), 329–337; Comput. Math. Math. Phys., 44:2 (2004), 309–316

Citation in format AMSBIB
\Bibitem{HemShiShi04}
\by P.~W.~Hemker, G.~I.~Shishkin, L.~P.~Shishkina
\paper High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2004
\vol 44
\issue 2
\pages 329--337
\mathnet{http://mi.mathnet.ru/zvmmf896}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2058255}
\zmath{https://zbmath.org/?q=an:1114.65128}
\transl
\jour Comput. Math. Math. Phys.
\yr 2004
\vol 44
\issue 2
\pages 309--316


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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. 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
    2. 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
    3. 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  adsnasa  isi  scopus
    4. Munyakazi J.B., Patidar K.C., “On Richardson extrapolation for fitted operator finite difference methods”, Applied Mathematics and Computation, 201:1–2 (2008), 465–480  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. G. I. Shishkin, L. P. Shishkina, “Improved difference scheme of the solution decomposition method for a singularly perturbed reaction-diffusion equation”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S197–S214  mathnet  crossref  isi  elib
    7. 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
    8. 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
    9. Mukherjee K., Natesan S., “Richardson extrapolation technique for singularly perturbed parabolic convection-diffusion problems”, Computing, 92:1 (2011), 1–32  crossref  mathscinet  zmath  isi  elib  scopus
    10. G. I. Shishkin, L. P. Shishkina, “Improved approximations of the solution and derivatives to a singularly perturbed reaction-diffusion equation based on the solution decomposition method”, Comput. Math. Math. Phys., 51:6 (2011), 1020–1049  mathnet  crossref  mathscinet  isi
    11. G. I. Shishkin, “A finite difference scheme of improved accuracy on a priori adapted grids for a singularly perturbed parabolic convection–diffusion equation”, Comput. Math. Math. Phys., 51:10 (2011), 1705–1728  mathnet  crossref  mathscinet  isi
    12. 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  scopus
    13. G. I. Shishkin, L. P. Shishkina, “Difference scheme of highest accuracy order for a singularly perturbed reaction-diffusion equation based on the solution decomposition method”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 262–275  mathnet  crossref  mathscinet  isi  elib
    14. G. I. Shishkin, L. P. Shishkina, “A higher order accurate solution decomposition scheme for a singularly perturbed parabolic reaction-diffusion equation”, Comput. Math. Math. Phys., 55:3 (2015), 386–409  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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