Shishkin, Grigorii I.; Shishkina, Lidia P. Difference schemes on uniform grids for an initial-boundary value problem for a singularly perturbed parabolic convection-diffusion equation. (English) Zbl 1454.35015 Comput. Methods Appl. Math. 20, No. 4, 709-715 (2020). MSC: 35B25 35K20 35A35 65M06 65M12 65M15 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{L. P. Shishkina}, Comput. Methods Appl. Math. 20, No. 4, 709--715 (2020; Zbl 1454.35015) Full Text: DOI
Shishkin, Grigorii; Shishkina, Lidia Improved computer scheme for a singularly perturbed parabolic convection-diffusion equation. (English) Zbl 1434.65134 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, 80-91 (2019). MSC: 65M06 65M22 65M12 PDFBibTeX XMLCite \textit{G. Shishkin} and \textit{L. Shishkina}, Lect. Notes Comput. Sci. 11386, 80--91 (2019; Zbl 1434.65134) Full Text: DOI
Clavero, C.; Gracia, J. L.; Shishkin, G. I.; Shishkina, L. P. An efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers. (English) Zbl 1357.65115 J. Comput. Appl. Math. 318, 634-645 (2017). MSC: 65M06 35K57 35B25 65M50 65M12 PDFBibTeX XMLCite \textit{C. Clavero} et al., J. Comput. Appl. Math. 318, 634--645 (2017; Zbl 1357.65115) Full Text: DOI
Shishkin, G. I. Difference scheme for a singularly perturbed parabolic convection-diffusion equation in the presence of perturbations. (English. Russian original) Zbl 1336.65142 Comput. Math. Math. Phys. 55, No. 11, 1842-1856 (2015); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 11, 1876-1892 (2015). MSC: 65M06 35K20 35B25 65M12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 55, No. 11, 1842--1856 (2015; Zbl 1336.65142); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 11, 1876--1892 (2015) Full Text: DOI
Shishkin, G. I. Standard scheme for a singularly perturbed parabolic convection-diffusion equation with computer perturbations. (English. Russian original) Zbl 1325.65126 Dokl. Math. 91, No. 3, 273-276 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 462, No. 1, 26-29 (2015). MSC: 65M06 35K20 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Dokl. Math. 91, No. 3, 273--276 (2015; Zbl 1325.65126); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 462, No. 1, 26--29 (2015) Full Text: DOI
Shishkin, G. I.; Shishkina, L. P. A higher order accurate solution decomposition scheme for a singularly perturbed parabolic reaction-diffusion equation. (English. Russian original) Zbl 1318.65056 Comput. Math. Math. Phys. 55, No. 3, 386-409 (2015); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 3, 393-416 (2015). MSC: 65M06 35B25 35K57 65M12 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{L. P. Shishkina}, Comput. Math. Math. Phys. 55, No. 3, 386--409 (2015; Zbl 1318.65056); translation from Zh. Vychisl. Mat. Mat. Fiz. 55, No. 3, 393--416 (2015) Full Text: DOI
Shishkina, L.; Shishkin, G. A technique to construct grid methods of higher accuracy order for a singularly perturbed parabolic reaction-diffusion equation. (English) Zbl 1319.65080 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, 139-151 (2014). MSC: 65M06 35K57 35B25 65M12 65M50 PDFBibTeX XMLCite \textit{L. Shishkina} and \textit{G. Shishkin}, Springer Proc. Math. Stat. 87, 139--151 (2014; Zbl 1319.65080) Full Text: DOI
Shishkin, Grigory; Shishkina, Lidia; Gracia, Jose Luis; Clavero, Carmelo On a numerical technique to study difference schemes for singularly perturbed parabolic reaction-diffusion equations. (English) Zbl 1315.65075 Int. J. Numer. Anal. Model. 11, No. 2, 412-426 (2014). MSC: 65M06 35B25 35K57 65M15 PDFBibTeX XMLCite \textit{G. Shishkin} et al., Int. J. Numer. Anal. Model. 11, No. 2, 412--426 (2014; Zbl 1315.65075) Full Text: Link
Shishkin, G. I. Computer difference scheme for a singularly perturbed convection-diffusion equation. (Russian, English) Zbl 1313.35173 Zh. Vychisl. Mat. Mat. Fiz. 54, No. 8, 1256-1269 (2014); translation in Comput. Math. Math. Phys. 54, No. 8, 1221-1233 (2014). MSC: 35K57 35K67 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 54, No. 8, 1256--1269 (2014; Zbl 1313.35173); translation in Comput. Math. Math. Phys. 54, No. 8, 1221--1233 (2014) Full Text: DOI
Shishkin, G. I. Conditioning and stability of finite difference schemes on uniform meshes for a singularly perturbed parabolic convection-diffusion equation. (Russian, English) Zbl 1299.35171 Zh. Vychisl. Mat. Mat. Fiz. 53, No. 4, 575-599 (2013); translation in Comput. Math. Math. Phys. 53, No. 4, 431-454 (2013). MSC: 35K57 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 53, No. 4, 575--599 (2013; Zbl 1299.35171); translation in Comput. Math. Math. Phys. 53, No. 4, 431--454 (2013) Full Text: DOI
Clavero, C.; Gracia, J. L.; Shishkin, G. I.; Shishkina, L. P. Grid approximation of a singularly perturbed parabolic equation with degenerating convective term and discontinuous right-hand side. (English) Zbl 1279.65098 Int. J. Numer. Anal. Model. 10, No. 4, 795-814 (2013). MSC: 65M06 35K20 35R05 35K65 65M12 65M15 35B25 PDFBibTeX XMLCite \textit{C. Clavero} et al., Int. J. Numer. Anal. Model. 10, No. 4, 795--814 (2013; Zbl 1279.65098) Full Text: Link
Miller, John J. H.; O’Riordan, Eugene; Shishkin, Grigorii I. Fitted numerical methods for singular perturbation problems. Error estimates in the maximum norm for linear problems in one and two dimensions. Revised ed. (English) Zbl 1243.65002 Hackensack, NJ: World Scientific (ISBN 978-981-4390-73-6/hbk; 978-981-4390-74-3/ebook). xiv, 176 p. (2012). MSC: 65-02 65M06 65M12 65M60 35B25 35K15 PDFBibTeX XMLCite \textit{J. J. H. Miller} et al., Fitted numerical methods for singular perturbation problems. Error estimates in the maximum norm for linear problems in one and two dimensions. Revised ed. Hackensack, NJ: World Scientific (2012; Zbl 1243.65002) Full Text: DOI
Shishkin, G. I. A finite difference scheme of improved accuracy on a priori adapted grids for a singularly perturbed parabolic convection-diffusion equation. (Russian, English) Zbl 1249.35163 Zh. Vychisl. Mat. Mat. Fiz. 51, No. 10, 1816-1839 (2011); translation in Comput. Math. Math. Phys. 51, No. 10, 1705-1728 (2011). MSC: 35K57 65M06 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 51, No. 10, 1816--1839 (2011; Zbl 1249.35163); translation in Comput. Math. Math. Phys. 51, No. 10, 1705--1728 (2011) Full Text: DOI
Shishkin, G. I. Approximation of singularly perturbed parabolic equations in unbounded domains subject to piecewise smooth boundary conditions in the case of solutions that grow at infinity. (Russian, English) Zbl 1224.35205 Zh. Vychisl. Mat. Mat. Fiz. 49, No. 10, 1827-1843 (2009); translation in Comput. Math., Math. Phys. 49, No. 10, 1748-1764 (2009). MSC: 35K57 65M06 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 49, No. 10, 1827--1843 (2009; Zbl 1224.35205); translation in Comput. Math., Math. Phys. 49, No. 10, 1748--1764 (2009) Full Text: DOI
Shishkin, G. I. Constructive and formal difference schemes for singularly perturbed parabolic equations in unbounded domains in the case of solutions growing at infinity. (English) Zbl 1185.65153 Russ. J. Numer. Anal. Math. Model. 24, No. 6, 591-617 (2009). Reviewer: Erwin Schechter (Moers) MSC: 65M06 65M12 65Y20 35K20 35B25 65M15 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Russ. J. Numer. Anal. Math. Model. 24, No. 6, 591--617 (2009; Zbl 1185.65153) Full Text: DOI
Shishkin, G. I.; Shishkina, L. P. Finite difference schemes for the singularly perturbed reaction-diffusion equation in the case of spherical symmetry. (Russian, English) Zbl 1199.65285 Comput. Math., Math. Phys. 49, No. 5, 810-826 (2009); translation from Zh. Vychisl. Mat. Mat. Fiz. 49, No. 5, 840-856 (2009). MSC: 65M06 35K57 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{L. P. Shishkina}, Zh. Vychisl. Mat. Mat. Fiz. 49, No. 5, 840--856 (2009; Zbl 1199.65285); translation from Zh. Vychisl. Mat. Mat. Fiz. 49, No. 5, 840--856 (2009) Full Text: DOI
Shishkin, G. I. The Richardson scheme for the singularly perturbed parabolic reaction-diffusion equation in the case of a discontinuous initial condition. (Russian, English) Zbl 1199.65284 Comput. Math., Math. Phys. 49, No. 8, 1348-1368 (2009); translation from Zh. Vychisl. Mat. Mat. Fiz. 49, No. 8, 1416-1436 (2009). MSC: 65M06 35K57 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 49, No. 8, 1416--1436 (2009; Zbl 1199.65284); translation from Zh. Vychisl. Mat. Mat. Fiz. 49, No. 8, 1416--1436 (2009) Full Text: DOI Link
Shishkina, L.; Shishkin, G. Conservative numerical method for a system of semilinear singularly perturbed parabolic reaction-diffusion equations. (English) Zbl 1172.65048 Math. Model. Anal. 14, No. 2, 211-228 (2009). MSC: 65M06 65M12 65M50 35K57 35B25 PDFBibTeX XMLCite \textit{L. Shishkina} and \textit{G. Shishkin}, Math. Model. Anal. 14, No. 2, 211--228 (2009; Zbl 1172.65048) Full Text: DOI
Shishkin, G. I. Numerical method for singularly perturbed parabolic equations in unbounded domains in the case of solutions growing at infinity. (English) Zbl 1162.65381 Comput. Methods Appl. Math. 9, No. 1, 100-110 (2009). MSC: 65M06 35B25 35K15 65M12 65M15 65M50 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Methods Appl. Math. 9, No. 1, 100--110 (2009; Zbl 1162.65381) Full Text: DOI
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 PDFBibTeX XMLCite \textit{G. Shishkin}, Lect. Notes Comput. Sci. 5434, 116--127 (2009; Zbl 1233.65060) Full Text: DOI
Shishkin, Grigory I.; Shishkina, Lidia P. Difference methods for singular perturbation problems. (English) Zbl 1163.65062 Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics 140. Boca Raton, FL: CRC Press (ISBN 978-1-58488-459-0/hbk; 978-0-203-49241-3/ebook). xv, 393 p. (2009). Reviewer: Srinivasan Natesan (Assam) MSC: 65M06 65M12 65N12 35B25 65-02 65N06 35J65 35K57 65M55 65N55 65M50 65N50 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{L. P. Shishkina}, Difference methods for singular perturbation problems. Boca Raton, FL: CRC Press (2009; Zbl 1163.65062) Full Text: DOI
Tselishcheva, I. V.; Shishkin, G. I. Sequential and parallel domain decomposition methods for a singularly perturbed parabolic convection-diffusion equation. (English. Russian original) Zbl 1237.65109 Proc. Steklov Inst. Math. 261, Suppl. 1, S206-S227 (2008); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 14, No. 1 (2008). MSC: 65M55 35B25 35K20 65M20 65Y05 65M12 PDFBibTeX XMLCite \textit{I. V. Tselishcheva} and \textit{G. I. Shishkin}, Proc. Steklov Inst. Math. 261, S206--S227 (2008; Zbl 1237.65109); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 14, No. 1 (2008) Full Text: DOI
Shishkin, Grigory I. A finite difference scheme on a priori adapted meshes for a singularly perturbed parabolic convection-diffusion equation. (English) Zbl 1174.65466 Numer. Math., Theory Methods Appl. 1, No. 2, 214-234 (2008). MSC: 65M06 35K20 35B25 65M50 65M12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Numer. Math., Theory Methods Appl. 1, No. 2, 214--234 (2008; Zbl 1174.65466)
Cordero, N.; Cronin, K.; Shishkin, G.; Shishkina, L.; Stynes, M. Finite difference scheme for a singularly perturbed parabolic equations in the presence of initial and boundary layers. (English) Zbl 1177.65121 Math. Model. Anal. 13, No. 4, 483-492 (2008). MSC: 65M06 65M15 65M12 35K57 65M50 35B25 PDFBibTeX XMLCite \textit{N. Cordero} et al., Math. Model. Anal. 13, No. 4, 483--492 (2008; Zbl 1177.65121) Full Text: DOI
Shishkin, G. I. Grid approximation of singularly perturbed parabolic equations with moving boundary layers. (English) Zbl 1177.65132 Math. Model. Anal. 13, No. 3, 421-442 (2008). MSC: 65M06 65M12 35B25 35K57 65M50 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Math. Model. Anal. 13, No. 3, 421--442 (2008; Zbl 1177.65132) Full Text: DOI
Shishkin, G. I. Grid approximation of a parabolic convection-diffusion equation on a priori adapted grids: \(\varepsilon\)-uniformly convergent schemes. (Russian, English) Zbl 1164.35314 Zh. Vychisl. Mat. Mat. Fiz. 48, No. 6, 1014-1033 (2008); translation in Comput. Math. Math. Phys. 48, No. 6, 956-974 (2008). MSC: 35B25 35K20 35K57 65N06 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 48, No. 6, 1014--1033 (2008; Zbl 1164.35314); translation in Comput. Math. Math. Phys. 48, No. 6, 956--974 (2008) Full Text: DOI
Shishkin, G. I. Conditioning of finite difference schemes for a singularly perturbed convection-diffusion parabolic equation. (Russian, English) Zbl 1164.35007 Zh. Vychisl. Mat. Mat. Fiz. 48, No. 5, 813-830 (2008); translation in Comput. Math. Math. Phys. 48, No. 5, 769-785 (2008). MSC: 35B25 35K20 65N06 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 48, No. 5, 813--830 (2008; Zbl 1164.35007); translation in Comput. Math. Math. Phys. 48, No. 5, 769--785 (2008) Full Text: DOI
Shishkina, L.; Shishkin, G. Robust numerical method for a system of singularly perturbed parabolic reaction-diffusion equations on a rectangle. (English) Zbl 1149.65074 Math. Model. Anal. 13, No. 2, 251-261 (2008). MSC: 65M06 35K57 35B25 65M12 65M15 PDFBibTeX XMLCite \textit{L. Shishkina} and \textit{G. Shishkin}, Math. Model. Anal. 13, No. 2, 251--261 (2008; Zbl 1149.65074)
Shishkin, G. Optimal difference schemes on piecewise-uniform meshes for a singularly perturbed parabolic convection-diffusion equation. (English) Zbl 1145.65059 Math. Model. Anal. 13, No. 1, 99-112 (2008). MSC: 65M06 35K15 65M50 PDFBibTeX XMLCite \textit{G. Shishkin}, Math. Model. Anal. 13, No. 1, 99--112 (2008; Zbl 1145.65059) Full Text: DOI
Shishkin, G. I. Necessary conditions for \(\varepsilon \)-uniform convergence of finite difference schemes for parabolic equations with moving boundary layers. (Russian. English summary) Zbl 07812342 Zh. Vychisl. Mat. Mat. Fiz. 47, No. 10, 1706-1726 (2007); translation in Comput. Math. Math. Phys. 47, No. 10, 1636-1655 (2007). MSC: 65M06 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 47, No. 10, 1706--1726 (2007; Zbl 07812342); translation in Comput. Math. Math. Phys. 47, No. 10, 1636--1655 (2007) Full Text: DOI MNR
Shishkin, G. I. Grid approximation of singularly perturbed parabolic equations with piecewise continuous initial-boundary conditions. (English. Russian original) Zbl 1237.65098 Proc. Steklov Inst. Math. 259, Suppl. 2, S213-S230 (2007); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 13, No. 2 (2007). MSC: 65M06 35K57 35B25 65M12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Proc. Steklov Inst. Math. 259, S213--S230 (2007; Zbl 1237.65098); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 13, No. 2 (2007) Full Text: DOI
Shishkin, G. I. A posteriori adaptive mesh technique with a priori error estimates for singularly perturbed semilinear parabolic convection-diffusion equations. (English) Zbl 1185.65217 Int. J. Comput. Sci. Math. 1, No. 2-4, 374-395 (2007). MSC: 65N30 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Int. J. Comput. Sci. Math. 1, No. 2--4, 374--395 (2007; Zbl 1185.65217) Full Text: DOI
Shishkin, G. Grid approximation of singularly perturbed parabolic reaction-diffusion equations with piecewise smooth initial-boundary conditions. (English) Zbl 1139.65065 Math. Model. Anal. 12, No. 2, 235-254 (2007). MSC: 65M06 65M12 65M50 35K57 35B25 PDFBibTeX XMLCite \textit{G. Shishkin}, Math. Model. Anal. 12, No. 2, 235--254 (2007; Zbl 1139.65065) Full Text: DOI
Shishkin, G. I. Using the technique of majorant functions in approximation of a singular perturbed parabolic convection-diffusion equation on adaptive grids. (English) Zbl 1124.65079 Russ. J. Numer. Anal. Math. Model. 22, No. 3, 263-289 (2007). MSC: 65M06 65M12 35K20 35B25 65M50 65M15 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Russ. J. Numer. Anal. Math. Model. 22, No. 3, 263--289 (2007; Zbl 1124.65079)
Li, S.; Shishkin, G. I.; Shishkina, L. P. Approximation of the solution and its derivative for the singularly perturbed Black-Scholes equation with nonsmooth initial data. (English) Zbl 1210.91134 Zh. Vychisl. Mat. Mat. Fiz. 47, No. 3, 460-480 (2007); translation in Comput. Math. Math. Phys. 47, No. 3, 442-462 (2007). MSC: 91G20 91G80 PDFBibTeX XMLCite \textit{S. Li} et al., Zh. Vychisl. Mat. Mat. Fiz. 47, No. 3, 460--480 (2007; Zbl 1210.91134); translation in Comput. Math. Math. Phys. 47, No. 3, 442--462 (2007) Full Text: DOI
Ansari, A. R.; Bakr, S. A.; Shishkin, G. I. A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations. (English) Zbl 1121.65090 J. Comput. Appl. Math. 205, No. 1, 552-566 (2007). Reviewer: Piotr Matus (Minsk) MSC: 65M06 65M12 65M50 35B25 35K20 35R10 PDFBibTeX XMLCite \textit{A. R. Ansari} et al., J. Comput. Appl. Math. 205, No. 1, 552--566 (2007; Zbl 1121.65090) Full Text: DOI
Shishkin, G. I. Grid approximation of singularly perturbed parabolic equations in the presence of weak and strong transient layers induced by a discontinuous right-hand side. (Russian, English) Zbl 1210.35145 Zh. Vychisl. Mat. Mat. Fiz. 46, No. 3, 407-420 (2006); translation in Comput. Math. Math. Phys. 46, No. 3, 388-401 (2006). MSC: 35K15 35B25 65L50 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 46, No. 3, 407--420 (2006; Zbl 1210.35145); translation in Comput. Math. Math. Phys. 46, No. 3, 388--401 (2006)
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 PDFBibTeX XMLCite \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)
Shishkin, G. I. Grid approximation of singularly perturbed parabolic convection-diffusion equations subject to a piecewise smooth initial condition. (Russian, English) Zbl 1210.35148 Zh. Vychisl. Mat. Mat. Fiz. 46, No. 1, 52-76 (2006); translation in Comput. Math. Math. Phys. 46, No. 1, 49-72 (2006). MSC: 35K20 34E15 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 46, No. 1, 52--76 (2006; Zbl 1210.35148); translation in Comput. Math. Math. Phys. 46, No. 1, 49--72 (2006)
O’Riordan, E.; Pickett, M. L.; Shishkin, G. I. Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems. (English) Zbl 1098.65091 Math. Comput. 75, No. 255, 1135-1154 (2006). Reviewer: S. Burys (Kraków) MSC: 65M06 65M15 65M12 35K15 35B25 65M50 PDFBibTeX XMLCite \textit{E. O'Riordan} et al., Math. Comput. 75, No. 255, 1135--1154 (2006; Zbl 1098.65091) Full Text: DOI
Shishkin, G. I. Grid approximation of parabolic convection-diffusion equations with piecewise smooth initial conditions. (English. Russian original) Zbl 1125.65334 Dokl. Math. 72, No. 3, 850-853 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 405, No. 1, 30-34 (2005). MSC: 65M06 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Dokl. Math. 72, No. 3, 850--853 (2005; Zbl 1125.65334); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 405, No. 1, 30--34 (2005)
Shishkin, G. I. Robust novel high-order accurate numerical methods for singularly perturbed convection-diffusion problems. (English) Zbl 1095.65089 Math. Model. Anal. 10, No. 4, 393-412 (2005). MSC: 65M06 35K15 35B25 65M12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Math. Model. Anal. 10, No. 4, 393--412 (2005; Zbl 1095.65089)
Shishkin, Grigory I.; Shishkina, Lidia P.; Hemker, Pieter W. A class of singularly perturbed convection-diffusion problems with a moving interior layer. An a posteriori adaptive mesh technique. (English) Zbl 1049.65085 Comput. Methods Appl. Math. 4, No. 1, 105-127 (2004). MSC: 65M06 35K15 35B25 65M12 65M15 65M50 PDFBibTeX XMLCite \textit{G. I. Shishkin} et al., Comput. Methods Appl. Math. 4, No. 1, 105--127 (2004; Zbl 1049.65085) Full Text: DOI
Shishkin, G. I. Limitations of adaptive mesh refinement techniques for singularly perturbed problems with a moving interior layer. (English) Zbl 1049.65101 J. Comput. Appl. Math. 166, No. 1, 267-280 (2004). MSC: 65M50 35B25 35K57 65M06 65M12 35K15 PDFBibTeX XMLCite \textit{G. I. Shishkin}, J. Comput. Appl. Math. 166, No. 1, 267--280 (2004; Zbl 1049.65101) Full Text: DOI
Shishkin, G. I. Discrete approximations of solutions and derivatives for a singularly perturbed parabolic convection–diffusion equation. (English) Zbl 1039.65061 J. Comput. Appl. Math. 166, No. 1, 247-266 (2004). MSC: 65M06 65M15 65M50 35B25 35K15 65M12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, J. Comput. Appl. Math. 166, No. 1, 247--266 (2004; Zbl 1039.65061) Full Text: DOI
O’Riordan, E.; Shishkin, G. I. Singularly perturbed parabolic problems with non-smooth data. (English) Zbl 1041.65071 J. Comput. Appl. Math. 166, No. 1, 233-245 (2004). Reviewer: K. T. S. Iyengar (Bangalore) MSC: 65M06 35K15 35R05 65M12 65M50 35B25 PDFBibTeX XMLCite \textit{E. O'Riordan} and \textit{G. I. Shishkin}, J. Comput. Appl. Math. 166, No. 1, 233--245 (2004; Zbl 1041.65071) Full Text: DOI
Miller, J. J. H.; Shishkin, G. I.; Koren, B.; Shishkina, L. P. Grid approximation of a singularly perturbed boundary value problem modelling heat transfer in the case of flow over a flat plate with suction of the boundary layer. (English) Zbl 1107.76371 J. Comput. Appl. Math. 166, No. 1, 221-232 (2004). MSC: 76M20 65L10 65L12 76D10 PDFBibTeX XMLCite \textit{J. J. H. Miller} et al., J. Comput. Appl. Math. 166, No. 1, 221--232 (2004; Zbl 1107.76371) Full Text: DOI
Shishkin, G. I. The grid approximation of a singularly perturbed parabolic equation on a composed domain with a moving boundary containing a concentrated source. (Russian, English) Zbl 1121.65347 Zh. Vychisl. Mat. Mat. Fiz. 43, No. 12, 1806-1824 (2003); translation in Comput. Math. Math. Phys. 43, No. 12, 1738-1755 (2003). Reviewer: Evgenij Nechaev (Moskva) MSC: 65M06 35B25 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 43, No. 12, 1806--1824 (2003; Zbl 1121.65347); translation in Comput. Math. Math. Phys. 43, No. 12, 1738--1755 (2003)
Shishkin, G. I. The Schwarz grid method for singularly perturbed convection-diffusion parabolic equations in the case of coherent and incoherent grids on subdomains. (Russian, English) Zbl 1105.49036 Zh. Vychisl. Mat. Mat. Fiz. 43, No. 2, 251-264 (2003); translation in Comput. Math. Math. Phys. 43, No. 2, 242-254 (2003). MSC: 49M27 65M06 35B25 35K57 65M12 65M55 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 43, No. 2, 251--264 (2003; Zbl 1105.49036); translation in Comput. Math. Math. Phys. 43, No. 2, 242--254 (2003)
Hemker, Pieter W.; Shishkin, Grigorii I.; Shishkina, Lidia P. Novel defect-correction high-order, in space and time, accurate schemes for parabolic singularly perturbed convection-diffusion problems. (English) Zbl 1034.65071 Comput. Methods Appl. Math. 3, No. 3, 387-404 (2003). MSC: 65M06 65M12 65M15 35B25 35K15 65M50 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., Comput. Methods Appl. Math. 3, No. 3, 387--404 (2003; Zbl 1034.65071) Full Text: DOI
Dunne, Raymond K.; O’Riordan, Eugene; Shishkin, Grigorii I. A fitted mesh method for a class of singularly perturbed parabolic problems with a boundary turning point. (English) Zbl 1036.65068 Comput. Methods Appl. Math. 3, No. 3, 361-372 (2003). Reviewer: Gerald W. Hedstrom (Pleasanton) MSC: 65M06 65M12 65M15 35B25 35K55 65M50 PDFBibTeX XMLCite \textit{R. K. Dunne} et al., Comput. Methods Appl. Math. 3, No. 3, 361--372 (2003; Zbl 1036.65068) Full Text: DOI
Shishkin, G. I. Grid approximation for a singularly perturbed parabolic reaction-diffusion equation with a moving concentrated source. (Russian. English summary) Zbl 1031.65097 Mat. Model. 15, No. 2, 43-61 (2003). Reviewer: S.G.Zhuravlev (Moskva) MSC: 65M06 35K57 80A20 80M20 65M12 65M50 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Mat. Model. 15, No. 2, 43--61 (2003; Zbl 1031.65097) Full Text: MNR
Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P. High-order time-accuracy schemes for parabolic singular perturbation problems with convection. (English) Zbl 1002.65092 Russ. J. Numer. Anal. Math. Model. 17, No. 1, 001-024 (2002). Reviewer: Marek Brandner (Plzeň) MSC: 65M06 65M12 35K15 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., Russ. J. Numer. Anal. Math. Model. 17, No. 1, 001--024 (2002; Zbl 1002.65092) Full Text: DOI Link
Hemker, Pieter W.; Shishkin, Grigorii I.; Shishkina, Lidia P. High-order time-accurate schemes for singularly perturbed parabolic convection-diffusion problems with Robin boundary conditions. (English) Zbl 0996.65081 Comput. Methods Appl. Math. 2, No. 1, 3-25 (2002). MSC: 65M06 65M12 65M15 35K15 35B25 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., Comput. Methods Appl. Math. 2, No. 1, 3--25 (2002; Zbl 0996.65081) Full Text: DOI Link
Shishkin, G. I. Grid approximations to singularly perturbed parabolic equations with turning points. (English. Russian original) Zbl 0998.65085 Differ. Equ. 37, No. 7, 1037-1050 (2001); translation from Differ. Uravn. 37, No. 7, 987-999 (2001). Reviewer: Z.Dżygadło (Warszawa) MSC: 65M06 35K65 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Differ. Equ. 37, No. 7, 1037--1050 (2001; Zbl 0998.65085); translation from Differ. Uravn. 37, No. 7, 987--999 (2001) Full Text: DOI
Samarskij, A. A.; Mazhukin, V. I.; Matus, P. P.; Shishkin, G. I. Monotone difference schemes for equations with mixed derivatives. (Russian. English summary) Zbl 1012.65103 Mat. Model. 13, No. 2, 17-26 (2001). Reviewer: Leonid B.Chubarov (Novosibirsk) MSC: 65N06 65M06 65M12 65N12 35J25 35K20 PDFBibTeX XMLCite \textit{A. A. Samarskij} et al., Mat. Model. 13, No. 2, 17--26 (2001; Zbl 1012.65103) Full Text: MNR
Shishkin, Grigorii I. A posteriori and a priori techniques of local grid refinement for parabolic problems with boundary and transition layers. (English) Zbl 0978.65090 Vulkov, Lubin (ed.) et al., Numerical analysis and its applications. 2nd international conference, NAA 2000, Rousse, Bulgaria, June 11-15, 2000. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 1988, 710-722 (2001). MSC: 65M50 35B25 65M12 65M15 35K57 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Lect. Notes Comput. Sci. 1988, 710--722 (2001; Zbl 0978.65090)
Hemker, Pieter W.; Shishkin, Grigorii I.; Shishkina, Lidia P. Acceleration by parallel computations of solving high-order time-accurate difference schemes for singularly perturbed convection-diffusion problems. (English) Zbl 0978.65077 Vulkov, Lubin (ed.) et al., Numerical analysis and its applications. 2nd international conference, NAA 2000, Rousse, Bulgaria, June 11-15, 2000. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 1988, 393-401 (2001). MSC: 65M06 65Y05 65M12 35B25 35K15 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., Lect. Notes Comput. Sci. 1988, 393--401 (2001; Zbl 0978.65077)
Dunne, R. K.; O’Riordan, E.; Shishkin, G. I. Singularly perturbed parabolic problems on non-rectangular domains. (English) Zbl 0978.65079 Vulkov, Lubin (ed.) et al., Numerical analysis and its applications. 2nd international conference, NAA 2000, Rousse, Bulgaria, June 11-15, 2000. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 1988, 265-272 (2001). MSC: 65M06 65M12 35B25 35K15 PDFBibTeX XMLCite \textit{R. K. Dunne} et al., Lect. Notes Comput. Sci. 1988, 265--272 (2001; Zbl 0978.65079)
Shishkin, G. I. A posteriori adaptive (by the gradient of the solution) grids for approximation of convection-diffusion singularly perturbed equations. (Russian. English summary) Zbl 0969.65088 Vychisl. Tekhnol. 6, No. 1, 72-87 (2001). Reviewer: V.Grebenev (Novosibirsk) MSC: 65M50 35K15 65M06 65M12 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Vychisl. Tekhnol. 6, No. 1, 72--87 (2001; Zbl 0969.65088)
Shishkin, G. I. A decomposition method for singularly perturbed parabolic convection-diffusion equations with discontinuous initial conditions. (Russian. English summary) Zbl 0969.65089 Sib. Zh. Vychisl. Mat. 4, No. 1, 85-106 (2001). Reviewer: V.Grebenev (Novosibirsk) MSC: 65M55 35K15 35B25 35R05 65M06 65M50 65M12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Sib. Zh. Vychisl. Mat. 4, No. 1, 85--106 (2001; Zbl 0969.65089)
Clavero, C.; Miller, J. J. H.; O’Riordan, E.; Shishkin, G. I. Numerical experiments for advection-diffusion problems in a channel with a \(180^\circ\) bend. (English) Zbl 1023.65112 Appl. Math. Comput. 118, No. 2-3, 223-246 (2001). MSC: 65N06 76D10 35B25 35J25 65N12 76M20 PDFBibTeX XMLCite \textit{C. Clavero} et al., Appl. Math. Comput. 118, No. 2--3, 223--246 (2001; Zbl 1023.65112) Full Text: DOI
Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P. High-order time-accurate parallel schemes for parabolic singularly perturbed problems with convection. (English) Zbl 0978.65076 Computing 66, No. 2, 139-161 (2001). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M06 35B25 35K15 65M12 65Y05 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., Computing 66, No. 2, 139--161 (2001; Zbl 0978.65076) Full Text: DOI
Shishkin, G. I. Approximation of systems of convection-diffusion elliptic equations with parabolic boundary layers. (English. Russian original) Zbl 1004.65106 Comput. Math. Math. Phys. 40, No. 11, 1582-1595 (2000); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 11, 1648-1661 (2000). Reviewer: Alexey Tret’yakov (Siedlce) MSC: 65N06 65N50 35B25 35J70 65N12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 40, No. 11, 1582--1595 (2000; Zbl 1004.65106); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 11, 1648--1661 (2000)
Shishkin, G. I.; Vabishchevich, P. N. Interpolation finite difference schemes on grids locally refined in time. (English) Zbl 0978.65078 Comput. Methods Appl. Mech. Eng. 190, No. 8-10, 889-901 (2000). Reviewer: Rémi Vaillancourt (Ottawa) MSC: 65M06 65M12 65M50 35K15 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{P. N. Vabishchevich}, Comput. Methods Appl. Mech. Eng. 190, No. 8--10, 889--901 (2000; Zbl 0978.65078) Full Text: DOI
Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P. Distributing the numerical solution of parabolic singularly perturbed problems with defect correction over independent processes. (Russian) Zbl 0956.65074 Sib. Zh. Vychisl. Mat. 3, No. 3, 229-258 (2000). Reviewer: V.Grebenev (Novosibirsk) MSC: 65M06 35K15 65Y05 35B25 65M12 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., Sib. Zh. Vychisl. Mat. 3, No. 3, 229--258 (2000; Zbl 0956.65074)
Farrell, P. A.; Hegarty, A. F.; Miller, J. J. H.; O’Riordan, E.; Shishkin, G. I. Robust computational techniques for boundary layers. (English) Zbl 0964.65083 Applied Mathematics and Mathematical Computation. 16. Boca Raton, FL: Chapman & Hall/ CRC Press. xvi, 254 p. (2000). Reviewer: Etienne Emmrich (Berlin) MSC: 65M06 35K57 65L12 65L10 65L20 65L70 35K15 34B05 34E15 65M15 35B25 65M12 76D10 76M20 65-02 PDFBibTeX XMLCite \textit{P. A. Farrell} et al., Robust computational techniques for boundary layers. Boca Raton, FL: Chapman \& Hall/ CRC Press (2000; Zbl 0964.65083)
Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P. \(\varepsilon\)-uniform schemes with high-order time-accuracy for parabolic singular perturbation problems. (English) Zbl 0942.65095 IMA J. Numer. Anal. 20, No. 1, 99-121 (2000). Reviewer: E.Emmrich (Berlin) MSC: 65M06 65M12 35K15 35B25 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., IMA J. Numer. Anal. 20, No. 1, 99--121 (2000; Zbl 0942.65095) Full Text: DOI Link
Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P. An \(\varepsilon\)-uniform defect-correction method for a parabolic convection-diffusion problem. (English) Zbl 0980.65089 Iliev, O. P. (ed.) et al., Recent advances in numerical methods and applications. Proceedings of the 4th international conference, NMA ’98, Sofia, Bulgaria, August 19-23, 1998. Singapore: World Scientific. 521-529 (1999). MSC: 65M06 65M50 65M12 35B25 35K15 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., in: Recent advances in numerical methods and applications. Proceedings of the 4th international conference, NMA '98, Sofia, Bulgaria, August 19--23, 1998. Singapore: World Scientific. 521--529 (1999; Zbl 0980.65089)
Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P. The numerical solution of a Neumann problem for parabolic singularly perturbed equations with high-order time accuracy. (English) Zbl 0980.65088 Iliev, O. P. (ed.) et al., Recent advances in numerical methods and applications. Proceedings of the 4th international conference, NMA ’98, Sofia, Bulgaria, August 19-23, 1998. Singapore: World Scientific. 27-39 (1999). MSC: 65M06 65M50 65M12 35B25 35K15 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., in: Recent advances in numerical methods and applications. Proceedings of the 4th international conference, NMA '98, Sofia, Bulgaria, August 19--23, 1998. Singapore: World Scientific. 27--39 (1999; Zbl 0980.65088)
Shishkin, G. I. Singularly perturbed boundary value problems with locally perturbed initial conditions: Equations with convective terms. (English. Russian original) Zbl 0964.35014 Comput. Math. Math. Phys. 39, No. 2, 249-265 (1999); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 2, 262-279 (1999). MSC: 35B25 65M06 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 39, No. 2, 249--265 (1999; Zbl 0964.35014); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 2, 262--279 (1999)
Shishkin, G. I.; Tselishcheva, I. V. Approximations of the solution and diffusion fluxes for singularly perturbed parabolic equations with convective terms on a strip. (English) Zbl 0968.65057 Samarskiĭ, A. A. (ed.) et al., Finite difference methods: theory and applications. Proceedings of the 1st conference on finite difference methods held in Rousse, Bulgaria, August 10-13, 1997. Commack, NY: Nova Science Publishers. 241-249 (1999). MSC: 65M06 35B25 65M12 65M30 35K15 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{I. V. Tselishcheva}, in: Finite difference methods: theory and applications. Proceedings of the 1st conference on finite difference methods held in Rousse, Bulgaria, August 10--13, 1997. Commack, NY: Nova Science Publishers. 241--249 (1999; Zbl 0968.65057)
Shishkin, Grigorii I. Grid approximation of singularly perturbed parabolic equations with convective terms in the case of impermeable walls. (English) Zbl 0968.65056 Samarskiĭ, A. A. (ed.) et al., Finite difference methods: theory and applications. Proceedings of the 1st conference on finite difference methods held in Rousse, Bulgaria, August 10-13, 1997. Commack, NY: Nova Science Publishers. 229-239 (1999). MSC: 65M06 35B25 65M12 65M50 35K15 PDFBibTeX XMLCite \textit{G. I. Shishkin}, in: Finite difference methods: theory and applications. Proceedings of the 1st conference on finite difference methods held in Rousse, Bulgaria, August 10--13, 1997. Commack, NY: Nova Science Publishers. 229--239 (1999; Zbl 0968.65056)
Shishkin, G. I. Improvement of accuracy of approximate solutions by correcting discrepancy for singularly perturbed equations with convective terms. (English. Russian original) Zbl 0983.65099 Russ. Math. 43, No. 5, 77-89 (1999); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1999, No. 5, 81-93 (1999). MSC: 65M06 35J25 35K20 65M12 65N06 65M50 65N50 65N12 PDFBibTeX XML
Shishkin, G. I. Locally one-dimensional difference schemes for singularly perturbed parabolic equations with convective terms. (English) Zbl 1161.65348 Russ. J. Numer. Anal. Math. Model. 14, No. 6, 495-511 (1999). MSC: 65M06 65M12 35K15 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Russ. J. Numer. Anal. Math. Model. 14, No. 6, 495--511 (1999; Zbl 1161.65348) Full Text: DOI
Shishkin, G. I. Grid approximation of parabolic equations with small parameters multiplying the space and time derivatives. Reaction-diffusion equations. (English) Zbl 1034.65506 Math. Balk., New Ser. 12, No. 1-2, 179-214 (1998). MSC: 65M06 35K15 35B25 65M12 65M50 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Math. Balk., New Ser. 12, No. 1--2, 179--214 (1998; Zbl 1034.65506)
Shishkin, G. I. A grid approximation for the Riemann problem in the case of the Burgers equation. (English. Russian original) Zbl 0972.65053 Comput. Math. Math. Phys. 38, No. 8, 1361-1363 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 8, 1418-1420 (1998). Reviewer: Alexey Tret’yakov (Siedlce) MSC: 65M06 35B25 35Q53 35K55 35R05 65M50 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 38, No. 8, 1361--1363 (1998; Zbl 0972.65053); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 8, 1418--1420 (1998)
Miller, J. J. H.; O’Riordan, E.; Shishkin, G. I.; Shishkina, L. P. Fitted mesh methods for problems with parabolic boundary layers. (English) Zbl 0934.65091 Math. Proc. R. Ir. Acad. 98A, No. 2, 173-190 (1998). MSC: 65M06 35B25 65M12 35K15 PDFBibTeX XMLCite \textit{J. J. H. Miller} et al., Math. Proc. R. Ir. Acad. 98A, No. 2, 173--190 (1998; Zbl 0934.65091)
Shishkin, G. I. Grid approximation of singularly perturbed systems of elliptic and parabolic equations with convective terms. (English. Russian original) Zbl 0951.65084 Differ. Equations 34, No. 12, 1693-1704 (1998); translation from Differ. Uravn. 34, No. 12, 1686-1696 (1998). MSC: 65M06 35B25 65M12 35K20 35L45 35J25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Differ. Equations 34, No. 12, 1693--1704 (1998; Zbl 0951.65084); translation from Differ. Uravn. 34, No. 12, 1686--1696 (1998)
Shishkin, G. I. Grid approximations of singularly perturbed systems for parabolic convection-diffusion equations with counterflow. (Russian) Zbl 0917.65079 Sib. Zh. Vychisl. Mat. 1, No. 3, 281-297 (1998). MSC: 65M06 65M50 65M12 35B25 35K55 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Sib. Zh. Vychisl. Mat. 1, No. 3, 281--297 (1998; Zbl 0917.65079)
Clavero, C.; Miller, John J. H.; O’Riordan, Eugene; Shishkin, Grigorii I. An accurate numerical solution of a two dimensional heat transfer problem with a parabolic boundary layer. (English) Zbl 0890.65105 J. Comput. Math. 16, No. 1, 27-39 (1998). Reviewer: E.Emmrich (Magdeburg) MSC: 65N06 65N50 65N12 35J25 PDFBibTeX XMLCite \textit{C. Clavero} et al., J. Comput. Math. 16, No. 1, 27--39 (1998; Zbl 0890.65105)
Shishkin, G. I. Grid approximation of a singularly perturbed Neumann problem for parabolic equations in the case of a discontinuous boundary function. (English. Russian original) Zbl 0946.65068 Comput. Math. Math. Phys. 37, No. 3, 370-373 (1997); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 3, 378-382 (1997). Reviewer: A.A.Tretiakov (Siedlce) MSC: 65M06 35K65 35B25 35R05 65M50 35K55 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 37, No. 3, 378--381 (1997; Zbl 0946.65068); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 3, 378--382 (1997)
Shishkin, G. I. Singularly perturbed boundary value problems with concentrated sources and discontinuous initial conditions. (English. Russian original) Zbl 0940.35104 Comput. Math. Math. Phys. 37, No. 4, 417-434 (1997); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 4, 429-446 (1997). Reviewer: Alexey A.Tretiakov (Siedlce) MSC: 35K20 39A10 35B25 65N12 35R05 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 37, No. 4, 429--446 (1997; Zbl 0940.35104); translation from Zh. Vychisl. Mat. Mat. Fiz. 37, No. 4, 429--446 (1997)
Shishkin, G. I.; Shishkina, L. P.; Hemker, P. W. A numerical method with floating meshes for singularly perturbed problems with a concentrated disturbance in the initial data. (English) Zbl 0908.65078 CWI Q. 10, No. 3-4, 317-336 (1997). MSC: 65M06 35B25 65M12 35K15 35L45 PDFBibTeX XMLCite \textit{G. I. Shishkin} et al., CWI Q. 10, No. 3--4, 317--336 (1997; Zbl 0908.65078)
Shishkin, G. I.; Tselishcheva, I. V. The decomposition method for singularly perturbed boundary value problems with the local perturbation of the initial conditions. Equations with convective terms. (English. Russian original) Zbl 0904.65097 Russ. Math. 41, No. 4, 96-105 (1997); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1997, No. 4(419), 98-107 (1997). Reviewer: Th.Sonar (Hamburg) MSC: 65M55 65M06 65M12 35B25 35K15 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{I. V. Tselishcheva}, Russ. Math. 41, No. 4, 96--105 (1997; Zbl 0904.65097); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1997, No. 4(419), 98--107 (1997)
Hemker, P. W.; Shishkin, G. I.; Shishkina, L. P. The use of defect correction for the solution of parabolic singular perturbation problems. (English) Zbl 0882.65071 Z. Angew. Math. Mech. 77, No. 1, 59-74 (1997). Reviewer: U.Langer (Linz) MSC: 65M06 35B25 35K15 65M12 65M50 PDFBibTeX XMLCite \textit{P. W. Hemker} et al., Z. Angew. Math. Mech. 77, No. 1, 59--74 (1997; Zbl 0882.65071) Full Text: DOI Link
Shishkin, G. I. Acceleration of the process of the numerical solution to singularly perturbed boundary value problems for parabolic equations on the basis of parallel computations. (English) Zbl 0880.65071 Russ. J. Numer. Anal. Math. Model. 12, No. 3, 271-291 (1997). Reviewer: Qin Mengzhao (Beijing) MSC: 65M06 65Y05 65M55 65M12 35K15 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Russ. J. Numer. Anal. Math. Model. 12, No. 3, 271--291 (1997; Zbl 0880.65071) Full Text: DOI
Shishkin, G. I. On finite difference fitted schemes for singularly perturbed boundary value problems with a parabolic boundary layer. (English) Zbl 0876.65075 J. Math. Anal. Appl. 208, No. 1, 181-204 (1997). Reviewer: E.Emmrich (Magdeburg) MSC: 65N06 35B25 35K20 35J25 65N12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, J. Math. Anal. Appl. 208, No. 1, 181--204 (1997; Zbl 0876.65075) Full Text: DOI
Shishkin, Grigorii I.; Vabishevich, Peter N. Parallel domain decomposition methods with the overlapping of subdomain for parabolic problems. (English) Zbl 0871.35007 Math. Models Methods Appl. Sci. 6, No. 8, 1169-1185 (1996). Reviewer: I.N.Molchanov (Kiev) MSC: 65M99 65N99 65M06 65M55 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin} and \textit{P. N. Vabishevich}, Math. Models Methods Appl. Sci. 6, No. 8, 1169--1185 (1996; Zbl 0871.35007) Full Text: DOI
Shishkin, G. I. Method of improving the accuracy of the approximate solutions to singularly perturbed equations by defect correction. (English) Zbl 0874.65065 Russ. J. Numer. Anal. Math. Model. 11, No. 6, 539-557 (1996). Reviewer: V.Makarov (Kiev) MSC: 65M06 35K15 35J25 35B25 65M12 65N06 65N12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Russ. J. Numer. Anal. Math. Model. 11, No. 6, 539--557 (1996; Zbl 0874.65065) Full Text: DOI
Farrell, P. A.; Hemker, P. W.; Shishkin, G. I. Discrete approximations for singularly perturbed boundary value problems with parabolic layers. III. (English) Zbl 1005.65093 J. Comput. Math. 14, No. 3, 273-290 (1996). Reviewer: Bernhard A.Schmitt (MR 98a:65114) MSC: 65M06 65M12 65M15 35B25 35K15 PDFBibTeX XMLCite \textit{P. A. Farrell} et al., J. Comput. Math. 14, No. 3, 273--290 (1996; Zbl 1005.65093)
Farrell, P. A.; Hemker, P. W.; Shishkin, G. I. Discrete approximations for singularly perturbed boundary value problems with parabolic layers. II. (English) Zbl 1005.65120 J. Comput. Math. 14, No. 2, 183-194 (1996). Reviewer: Bernhard A.Schmitt (MR 98a:65150) MSC: 65N06 65N12 35J25 35B25 PDFBibTeX XMLCite \textit{P. A. Farrell} et al., J. Comput. Math. 14, No. 2, 183--194 (1996; Zbl 1005.65120)
Farrell, P. A.; Hemker, P. W.; Shishkin, G. I. Discrete approximations for singularly perturbed boundary value problems with parabolic layers. I. (English) Zbl 0839.65091 J. Comput. Math. 14, No. 1, 71-97 (1996). Reviewer: P.Chocholatý (Bratislava) MSC: 65M06 35B25 35K15 65M12 PDFBibTeX XMLCite \textit{P. A. Farrell} et al., J. Comput. Math. 14, No. 1, 71--97 (1996; Zbl 0839.65091)
Shishkin, G. I. Approximation of the solutions and diffusion flows of singularly perturbed boundary-value problems with discontinuous initial conditions. (English. Russian original) Zbl 0915.65098 Comput. Math. Math. Phys. 36, No. 9, 1233-1250 (1996); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 9, 83-104 (1996). MSC: 65M06 65M15 35B25 35K15 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 36, No. 9, 1233--1250 (1996; Zbl 0915.65098); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 9, 83--104 (1996)
Miller, John J. H.; O’Riordan, Eugene; Shishkin, Grigorii I. Fitted numerical methods for singular perturbation problems. Error estimates in the maximum norm for linear problems in one and two dimensions. (English) Zbl 0915.65097 Singapore: World Scientific. xiv, 166 p. (1996). Reviewer: H.Marcinkowska (Wrocław) MSC: 65M06 65F10 65-02 35B25 35K15 65M60 65M12 PDFBibTeX XMLCite \textit{J. J. H. Miller} et al., Fitted numerical methods for singular perturbation problems. Error estimates in the maximum norm for linear problems in one and two dimensions. Singapore: World Scientific (1996; Zbl 0915.65097)
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 PDFBibTeX XMLCite \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. Grid approximation of quasi-linear singularly perturbed elliptic and parabolic equations with mixed boundary conditions. (Russian. English summary) Zbl 0978.65080 Mat. Model. 7, No. 10, 111-126 (1995). MSC: 65M06 35B25 65M12 65N12 35K55 35J65 65N06 65N50 65M50 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Mat. Model. 7, No. 10, 111--126 (1995; Zbl 0978.65080) Full Text: MNR
Shishkin, G. I. A difference scheme for the disconitnuity decomposition problem in the case of Burgers’ viscous equation. (English. Russian original) Zbl 0875.65081 Dokl. Math. 51, No. 3, 362-366 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 342, No. 3, 313-317 (1995). MSC: 65M06 35Q53 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Dokl. Math. 51, No. 3, 362--366 (1995; Zbl 0875.65081); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 342, No. 3, 313--317 (1995)
Shishkin, G. I. The method of additive separation of singularities for quasilinear singularly perturbed elliptic and parabolic equations. (English. Russian original) Zbl 0843.65073 Comput. Math. Math. Phys. 34, No. 12, 1541-1558 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 12, 1793-1814 (1994). Reviewer: M.Jung (Chemnitz) MSC: 65N06 35J65 35K55 65M06 65N12 65M12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 34, No. 12, 1541--1558 (1994; Zbl 0843.65073); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 12, 1793--1814 (1994)
Shishkin, G. I. A grid approximation of singularly perturbed quasilinear elliptic and parabolic equations which degenerate into equations without spatial derivatives. (English. Russian original) Zbl 0832.65094 Comput. Math. Math. Phys. 34, No. 11, 1403-1419 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 11, 1632-1651 (1994). MSC: 65M06 65N06 65H10 35K55 35J65 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Comput. Math. Math. Phys. 34, No. 11, 1403--1419 (1994; Zbl 0832.65094); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 11, 1632--1651 (1994)