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 Zh. Vychisl. Mat. Mat. Fiz., 1991, Volume 31, Number 12, Pages 1808–1825 (Mi zvmmf2971)

Grid approximation of a singularly perturbed boundary-value problem for a quasi-linear elliptic equation in the completely degenerate case

G. I. Shishkin

Sverdlovsk

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English version:
USSR Computational Mathematics and Mathematical Physics, 1991, 31:12, 33–46

Bibliographic databases:
UDC: 519.633
MSC: Primary 65N06; Secondary 65N12, 35J70, 35B25

Citation: G. I. Shishkin, “Grid approximation of a singularly perturbed boundary-value problem for a quasi-linear elliptic equation in the completely degenerate case”, Zh. Vychisl. Mat. Mat. Fiz., 31:12 (1991), 1808–1825; U.S.S.R. Comput. Math. Math. Phys., 31:12 (1991), 33–46

Citation in format AMSBIB
\Bibitem{Shi91} \by G.~I.~Shishkin \paper Grid approximation of a singularly perturbed boundary-value problem for a quasi-linear elliptic equation in the completely degenerate case \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 1991 \vol 31 \issue 12 \pages 1808--1825 \mathnet{http://mi.mathnet.ru/zvmmf2971} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1147898} \zmath{https://zbmath.org/?q=an:0780.65063} \transl \jour U.S.S.R. Comput. Math. Math. Phys. \yr 1991 \vol 31 \issue 12 \pages 33--46 \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991KG16100005} 

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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, “Mesh approximation of singularly perturbed quasilinear elliptic equations which degenerate to a zero-order equation”, Comput. Math. Math. Phys., 33:9 (1993), 1155–1170
2. G. I. Shishkin, “The method of additive separation of singularities for quasilinear singularly perturbed elliptic and parabolic equations”, Comput. Math. Math. Phys., 34:12 (1994), 1541–1558
3. G. I. Shishkin, “A grid approximation of singularly perturbed quasilinear elliptic and parabolic equations which degenerate into equations without spatial derivatives”, Comput. Math. Math. Phys., 34:11 (1994), 1403–1419
4. 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
5. G. I. Shishkin, “Approximation of the solutions and diffusion flows of singularly perturbed boundary-value problems with discontinuous initial conditions”, Comput. Math. Math. Phys., 36:9 (1996), 1233–1250
6. G. I. Shishkin, “Grid approximation of parabolic equations with singular initial conditions”, Comput. Math. Math. Phys., 36:3 (1996), 341–356
7. G. I. Shishkin, “Singularly perturbed boundary value problems with concentrated sources and discontinuous initial conditions”, Comput. Math. Math. Phys., 37:4 (1997), 417–434
8. G. I. Shishkin, “Grid approximation of a singularly perturbed Neumann problem for parabolic equations in the case of a discontinuous boundary function”, Comput. Math. Math. Phys., 37:3 (1997), 370–373
9. G. I. Shishkin, “Finite-difference approximations for singularly perturbed elliptic equations”, Comput. Math. Math. Phys., 38:12 (1998), 1909–1921
10. G. I. Shishkin, “Singularly perturbed boundary value problems with locally perturbed initial conditions: Equations with convective terms”, Comput. Math. Math. Phys., 39:2 (1999), 249–265
11. G. I. Shishkin, “Approximation of systems of convection-diffusion elliptic equations with parabolic boundary layers”, Comput. Math. Math. Phys., 40:11 (2000), 1582–1595
12. G. I. Shishkin, “Grid approximation of singularly perturbed parabolic convection-diffusion equations with a piecewise-smooth initial condition”, Comput. Math. Math. Phys., 46:1 (2006), 49–72
13. G. I. Shishkin, “Grid approximation of singularly perturbed parabolic equations with piecewise continuous initial-boundary conditions”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S213–S230
14. Shishkin G.I., “Grid approximation of singularly perturbed parabolic reaction-diffusion equations with piecewise smooth initial-boundary conditions”, Mathematical Modelling and Analysis, 12:2 (2007), 235–254
15. G. I. Shishkin, L. P. Shishkina, “Finite difference schemes for the singularly perturbed reaction-diffusion equation in the case of spherical symmetry”, Comput. Math. Math. Phys., 49:5 (2009), 810–826
16. 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
17. Shishkin G.I., “Constructive and formal difference schemes for singularly perturbed parabolic equations in unbounded domains in the case of solutions growing at infinity”, Russian Journal of Numerical Analysis and Mathematical Modelling, 24:6 (2009), 591–617
18. G. I. Shishkin, L. P. Shishkina, “A conservative difference scheme for a singularly perturbed elliptic reaction-diffusion equation: approximation of solutions and derivatives”, Comput. Math. Math. Phys., 50:4 (2010), 633–645
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