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Tselishcheva, Irina; Shishkin, Grigorii
On a reliable numerical method for a singularly perturbed parabolic reaction-diffusion problem in a doubly connected domain. (English) Zbl 1434.65139
Dimov, Ivan (ed.) et al., Finite difference methods. Theory and applications. 7th international conference, FDM 2018, Lozenetz, Bulgaria, June 11–16, 2018. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 11386, 558-565 (2019).
MSC:  65M06 65M50 65M55 65M12
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\textit{I. Tselishcheva} and \textit{G. Shishkin}, Lect. Notes Comput. Sci. 11386, 558--565 (2019; Zbl 1434.65139)
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Lanza de Cristoforis, M.; Musolino, P.
A functional analytic approach to homogenization problems. (English) Zbl 06567038
Constanda, Christian (ed.) et al., Integral methods in science and engineering. Theoretical and computational advances. Papers based on the presentations at the international conference, IMSE, Karlsruhe, Germany, July 21–25, 2014. Cham: Birkhäuser/Springer (ISBN 978-3-319-16726-8/hbk; 978-3-319-16727-5/ebook). 353-359 (2015).
MSC:  74
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\textit{M. Lanza de Cristoforis} and \textit{P. Musolino}, in: Integral methods in science and engineering. Theoretical and computational advances. Papers based on the presentations at the international conference, IMSE, Karlsruhe, Germany, July 21--25, 2014. Cham: Birkhäuser/Springer. 353--359 (2015; Zbl 06567038)
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Shishkin, G.; Shishkina, L.; Petrenko, A.
Standard difference scheme for a singularly perturbed convection-diffusion equation in the presence of perturbations. (English) Zbl 1319.65068
Ansari, Ali R. (ed.), Advances in applied mathematics. Selected papers based on the presentations at the 1st Gulf international conference on applied mathematics 2013, GICAM ’13, Kuwait City, Kuwait, in cooperation with the Society for Industrial and Applied Mathematics, SIAM, November 19–21, 2013. Cham: Springer (ISBN 978-3-319-06922-7/hbk; 978-3-319-06923-4/ebook). Springer Proceedings in Mathematics & Statistics 87, 41-55 (2014).
MSC:  65L12 65L10 34B05 65L11 65L20
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\textit{G. Shishkin} et al., in: Advances in applied mathematics. Selected papers based on the presentations at the 1st Gulf international conference on applied mathematics 2013, GICAM '13, Kuwait City, Kuwait, in cooperation with the Society for Industrial and Applied Mathematics, SIAM, November 19--21, 2013. Cham: Springer. 41--55 (2014; Zbl 1319.65068)
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Musolino, Paolo
A singularly perturbed Dirichlet problem for the Poisson equation in a periodically perforated domain. A functional analytic approach. (English) Zbl 1266.35039
Almeida, Alexandre (ed.) et al., Advances in harmonic analysis and operator theory. The Stefan Samko anniversary volume on the occasion of his 70th birthday. Mainly based on the presentations at two conferences, Lisbon and Aveiro, Portugal, in June – July, 2011. Basel: Birkhäuser (ISBN 978-3-0348-0515-5/hbk; 978-3-0348-0516-2/ebook). Operator Theory: Advances and Applications 229, 269-289 (2013).
MSC:  35J25 31B10 45A05 47H30 35J05
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\textit{P. Musolino}, Oper. Theory: Adv. Appl. 229, 269--289 (2013; Zbl 1266.35039)
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Shishkin, G. I.; Shishkina, L. P.
Improved difference scheme of the solution decomposition method for a singularly perturbed reaction-diffusion equation. (English. Russian original) Zbl 1227.65067
Proc. Steklov Inst. Math. 272, Suppl. 1, 197-214 (2011); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 16, No. 1, 255-271 (2010).
MSC:  65L12 65L11 34B10 34E15 65L20
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\textit{G. I. Shishkin} and \textit{L. P. Shishkina}, Proc. Steklov Inst. Math. 272, 197--214 (2011; Zbl 1227.65067); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 16, No. 1, 255--271 (2010)
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Shishkin, Grigory
Improved difference scheme for a singularly perturbed parabolic reaction-diffusion equation with discontinuous initial condition. (English) Zbl 1233.65060
Margenov, Svetozar (ed.) et al., Numerical analysis and its applications. 4th international conference, NAA 2008, Lozenetz, Bulgaria, June 16–20, 2008. Revised selected papers. Berlin: Springer (ISBN 978-3-642-00463-6/pbk). Lecture Notes in Computer Science 5434, 116-127 (2009).
MSC:  65M06 35B25 35K57
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\textit{G. Shishkin}, Lect. Notes Comput. Sci. 5434, 116--127 (2009; Zbl 1233.65060)
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Shishkin, G. I.
A method of asymptotic constructions with improved accuracy for quasilinear singularly perturbed parabolic convection-diffusion equation. (Russian, English) Zbl 1210.65143
Zh. Vychisl. Mat. Mat. Fiz. 46, No. 2, 242-261 (2006); translation in Comput. Math. Math. Phys. 46, No. 2, 231-250 (2006).
MSC:  65L50 35B25
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\textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 46, No. 2, 242--261 (2006; Zbl 1210.65143); translation in Comput. Math. Math. Phys. 46, No. 2, 231--250 (2006)
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Lanza de Cristoforis, Massimo
A singular perturbation Dirichlet boundary value problem for harmonic functions on a domain with a small hole. (English) Zbl 1126.35010
Kazama, Hideaki (ed.) et al., Proceedings of the 12th international conference on finite or infinite dimensional complex analysis and applications, ICFIDCAA, Tokyo, Japan, July 27– 31, 2004. Fukuoka: Kyushu University Press (ISBN 4-87378-899-4/pbk). 205-212 (2005).
Reviewer: Dagmar Medková (Praha)
MSC:  35J05 35J25 31A25
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\textit{M. Lanza de Cristoforis}, in: Proceedings of the 12th international conference on finite or infinite dimensional complex analysis and applications, ICFIDCAA, Tokyo, Japan, July 27-- 31, 2004. Fukuoka: Kyushu University Press. 205--212 (2005; Zbl 1126.35010)
Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P.
High-order accurate decomposition of the Richardson method for a singularly perturbed elliptic reaction-diffusion equation. (Russian, English) Zbl 1114.65128
Zh. Vychisl. Mat. Mat. Fiz. 44, No. 2, 329-337 (2004); translation in Comput. Math. Math. Phys. 44, No. 2, 309-316 (2004).
Reviewer: Evgenij Nechaev (Moskva)
MSC:  65N06 35B25 35J25 65N15 65N55
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\textit{P. W. Hemker} et al., Zh. Vychisl. Mat. Mat. Fiz. 44, No. 2, 329--337 (2004; Zbl 1114.65128); translation in Comput. Math. Math. Phys. 44, No. 2, 309--316 (2004)
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Denisov, I. V.
A corner boundary layer in nonmonotone singularly perturbed boundary value problems with nonlinearities. (Russian, English) Zbl 1136.35359
Zh. Vychisl. Mat. Mat. Fiz. 44, No. 9, 1674-1692 (2004); translation in Comput. Math. Math. Phys. 44, No. 9, 1592-1610 (2004).
Reviewer: Elena Glukhova (Moskva)
MSC:  35J60 35B25
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\textit{I. V. Denisov}, Zh. Vychisl. Mat. Mat. Fiz. 44, No. 9, 1674--1692 (2004; Zbl 1136.35359); translation in Comput. Math. Math. Phys. 44, No. 9, 1592--1610 (2004)
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Butuzov, V. F.; Kryazhimskiĭ, S. A.; Nedel’ko, I. V.
On the global domain of influence of stable steplike contrast structures in the Dirichlet problem. (Russian, English) Zbl 1072.35538
Zh. Vychisl. Mat. Mat. Fiz. 44, No. 6, 1039-1061 (2004); translation in Comput. Math. Math. Phys. 44, No. 6, 985-1006 (2004).
MSC:  35K55 35B25 35B40
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\textit{V. F. Butuzov} et al., Zh. Vychisl. Mat. Mat. Fiz. 44, No. 6, 1039--1061 (2004; Zbl 1072.35538); translation in Comput. Math. Math. Phys. 44, No. 6, 985--1006 (2004)
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Denisov, I. V.
The corner boundary layer in nonlinear singularly perturbed elliptic equations. (English. Russian original) Zbl 1114.35304
Comput. Math. Math. Phys. 41, No. 3, 362-378 (2001); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 3, 390-406 (2001).
Reviewer: Alexey Tret’yakov (Siedlce)
MSC:  35B25 35C20 35J60 35J65
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\textit{I. V. Denisov}, Comput. Math. Math. Phys. 41, No. 3, 362--378 (2001; Zbl 1114.35304); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 3, 390--406 (2001)
Shishkin, G. I.
Approximation of singularly perturbed elliptic equations with convective terms in the case of a flow impinging on an impermeable wall. (English. Russian original) Zbl 0970.35018
Comput. Math. Math. Phys. 38, No. 11, 1768-1782 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 11, 1844-1859 (1998).
Reviewer: Alexey Tret’yakov (Siedlce)
MSC:  35J25 35B25 65N12
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\textit{G. I. Shishkin}, Comput. Math. Math. Phys. 38, No. 11, 1768--1782 (1998; Zbl 0970.35018); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 11, 1844--1859 (1998)
Shishkin, G. I.
Mesh approximation of singularly perturbed boundary-value problems for systems of elliptic and parabolic equations. (English. Russian original) Zbl 0852.65071
Comput. Math. Math. Phys. 35, No. 4, 429-446 (1995); translation from Zh. Vychisl. Mat. Mat. Fiz. 35, No. 4, 542-564 (1995).
MSC:  65M06 35K15 35M10 35J25
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\textit{G. I. Shishkin}, Comput. Math. Math. Phys. 35, No. 4, 429--446 (1995; Zbl 0852.65071); translation from Zh. Vychisl. Mat. Mat. Fiz. 35, No. 4, 542--564 (1995)
Shishkin, G. I.
Lattice approximation of singularly perturbed degenerate elliptic equations. (English. Russian original) Zbl 0815.65109
Comput. Math. Math. Phys. 33, No. 4, 493-509 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 4, 541-560 (1993).
Reviewer: E.D’yakonov (Moskva)
MSC:  65N06 65N12 35J25 35B25 35J70
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\textit{G. I. Shishkin}, Comput. Math. Math. Phys. 33, No. 4, 541--560 (1993; Zbl 0815.65109); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 4, 541--560 (1993)
Shishkin, G. I.
Approximation of the solutions of singularly perturbed boundary value problems with a parabolic boundary layer. (English. Russian original) Zbl 0709.65073
U.S.S.R. Comput. Math. Math. Phys. 29, No. 4, 1-10 (1989); translation from Zh. Vychisl. Mat. Mat. Fiz. 29, No. 7, 963-977 (1989).
MSC:  65N12 65N06 35K20 35B25
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\textit{G. I. Shishkin}, U.S.S.R. Comput. Math. Math. Phys. 29, No. 4, 1--10 (1989; Zbl 0709.65073); translation from Zh. Vychisl. Mat. Mat. Fiz. 29, No. 7, 963--977 (1989)
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Shishkin, G. I.
Approximation of solutions of singularly perturbed boundary-value problems with a corner boundary layer. (English. Russian original) Zbl 0663.65094
U.S.S.R. Comput. Math. Math. Phys. 27, No. 5, 54-63 (1987); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 9, 1360-1374 (1987).
MSC:  65N12 65N15 35K10 35J25 35B25
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\textit{G. I. Shishkin}, U.S.S.R. Comput. Math. Math. Phys. 27, No. 5, 54--63 (1987; Zbl 0663.65094); translation from Zh. Vychisl. Mat. Mat. Fiz. 27, No. 9, 1360--1374 (1987)
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