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, 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
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
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
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)
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
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)
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 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)
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. 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)
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, 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. 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. 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. 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. 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
Hemker, P. W.; Shishkin, G. I. Approximation of parabolic PDEs with a discontinuous initial condition. (English) Zbl 0835.65101 East-West J. Numer. Math. 1, No. 4, 287-302 (1993). MSC: 65M06 65M12 35K20 PDFBibTeX XMLCite \textit{P. W. Hemker} and \textit{G. I. Shishkin}, East-West J. Numer. Math. 1, No. 4, 287--302 (1993; Zbl 0835.65101)
Shishkin, G. I. On the approximation of solutions of boundary value problems with parabolic boundary layer. (Russian) Zbl 0715.65064 Numerical analysis and mathematical modelling, Banach Cent. Publ. 24, 435-443 (1990). Reviewer: L.P.Lebedev MSC: 65M06 65N06 65M55 35K20 35J25 PDFBibTeX XML
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 PDFBibTeX XMLCite \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) Full Text: DOI
Shishkin, G. I. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous coefficients and concentrated factors. (Russian) Zbl 0691.65070 Zh. Vychisl. Mat. Mat. Fiz. 29, No. 9, 1277-1290 (1989). Reviewer: R.D.Lazarov MSC: 65N12 65N06 35B25 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 29, No. 9, 1277--1290 (1989; Zbl 0691.65070)
Shishkin, G. I. Approximation of the solutions of singularly perturbed boundary value problems with parabolic boundary layer. (Russian) Zbl 0683.65086 Zh. Vychisl. Mat. Mat. Fiz. 29, No. 7, 963-977 (1989). Reviewer: M.Z.Qin MSC: 65N12 65N06 35K20 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 29, No. 7, 963--977 (1989; Zbl 0683.65086)
Shishkin, G. I. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous boundary conditions. (English. Russian original) Zbl 0698.65058 U.S.S.R. Comput. Math. Math. Phys. 28, No. 6, 32-41 (1988); translation from Zh. Vychisl. Mat. Mat. Fiz. 28, No. 11, 1649-1662 (1988). MSC: 65N06 65N12 35K20 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, U.S.S.R. Comput. Math. Math. Phys. 28, No. 6, 32--41 (1988; Zbl 0698.65058); translation from Zh. Vychisl. Mat. Mat. Fiz. 28, No. 11, 1649--1662 (1988) Full Text: DOI
Shishkin, G. I. Approximation for solutions of singularly perturbed boundary value problems with a corner boundary layer. (English. Russian original) Zbl 0682.35011 Sov. Math., Dokl. 36, No. 2, 240-244 (1988); translation from Dokl. Akad. Nauk SSSR 269, 39-43 (1987). Reviewer: C.M.Brauner MSC: 35B25 35K20 35J25 65M99 65N99 65N06 65N12 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Sov. Math., Dokl. 36, No. 2, 240--244 (1988; Zbl 0682.35011); translation from Dokl. Akad. Nauk SSSR 269, 39--43 (1987)
Shishkin, G. I. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous initial condition. (English. Russian original) Zbl 0662.65087 Sov. Math., Dokl. 37, 792-796 (1988); translation from Dokl. Akad. Nauk SSSR 300, No. 5, 1066-1070 (1988). Reviewer: I.Evzerov MSC: 65N06 65N12 35B25 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Sov. Math., Dokl. 37, 792--796 (1988; Zbl 0662.65087); translation from Dokl. Akad. Nauk SSSR 300, No. 5, 1066--1070 (1988)
Shishkin, G. I. A difference scheme for a singularly perturbed equation of parabolic type with discontinuous boundary condition. (Russian) Zbl 0662.65086 Zh. Vychisl. Mat. Mat. Fiz. 28, No. 11, 1649-1662 (1988). Reviewer: S.Gocheva-Ilieva MSC: 65N06 65N12 35K20 35B25 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 28, No. 11, 1649--1662 (1988; Zbl 0662.65086)
Shishkin, G. I. A method of improving the accuracy of the solutions of difference schemes for parabolic equations with a small parameter in the highest derivative. (English) Zbl 0582.65074 U.S.S.R. Comput. Math. Math. Phys. 24, No. 3, 150-157 (1984). MSC: 65N12 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, U.S.S.R. Comput. Math. Math. Phys. 24, No. 3, 150--157 (1984; Zbl 0582.65074) Full Text: DOI
Shishkin, G. I. The solution of a boundary value problem for an equation of second order in a domain with a small perforation for the case of circular symmetry. (Russian) Zbl 0579.65103 Differential equations with small parameter, Collect. Artic., Sverdlovsk 1984, 104-118 (1984). Reviewer: K.Barckow MSC: 65N12 35K20 PDFBibTeX XML
Shishkin, G. I. Increasing the accuracy of solutions of difference schemes for parabolic equations with a small parameter at the highest derivative. (Russian) Zbl 0565.65057 Zh. Vychisl. Mat. Mat. Fiz. 24, No. 6, 864-875 (1984). Reviewer: R.Farzan MSC: 65N12 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Zh. Vychisl. Mat. Mat. Fiz. 24, No. 6, 864--875 (1984; Zbl 0565.65057)
Shishkin, G. I. A difference scheme on a non-uniform mesh for a differential equation with a small parameter in the highest derivative. (English. Russian original) Zbl 0545.65062 U.S.S.R. Comput. Math. Math. Phys. 23, No. 3, 59-66 (1983); translation from Zh. Vychisl. Mat. Mat. Fiz. 23, No. 3, 609-619 (1983). Reviewer: L.Bakule MSC: 65L10 65N22 34B05 34E15 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, U.S.S.R. Comput. Math. Math. Phys. 23, No. 3, 59--66 (1983; Zbl 0545.65062); translation from Zh. Vychisl. Mat. Mat. Fiz. 23, No. 3, 609--619 (1983) Full Text: DOI
Shishkin, G. I. A Stefan problem with one of the phases disappearing. (English) Zbl 0366.35047 Differ. Equations 12(1976), 1596-1597 (1977). MSC: 35K20 35A05 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Differ. Equations 12, 1596--1597 (1977; Zbl 0366.35047)
Shishkin, G. I. Über ein Problem Stefanschen Typs mit Verschwinden einer der Phasen. (Russian) Zbl 0336.35055 Differ. Uravn. 12, 2283-2284 (1976). MSC: 35K20 35A05 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Differ. Uravn. 12, 2283--2284 (1976; Zbl 0336.35055)
Shishkin, G. I. On a problem of Stefan type with discontinuous moving boundary. (English. Russian original) Zbl 0328.35034 Sov. Math., Dokl. 16, 1409-1412 (1975); translation from Dokl. Akad. Nauk SSSR 224, 1276-1278 (1975). MSC: 35K05 35K20 PDFBibTeX XMLCite \textit{G. I. Shishkin}, Sov. Math., Dokl. 16, 1409--1412 (1975; Zbl 0328.35034); translation from Dokl. Akad. Nauk SSSR 224, 1276--1278 (1975)
Il’in, A. M.; Shishkin, G. I. Erstes Randwertproblem für die Gleichung der Brownschen Bewegung auf einer Halbgeraden. (Russian) Zbl 0319.60053 Mat. Zap., Sverdl. 7, No. 2, 59-75 (1969). MSC: 60J65 35K20 PDFBibTeX XMLCite \textit{A. M. Il'in} and \textit{G. I. Shishkin}, Mat. Zap., Sverdl. 7, No. 2, 59--75 (1969; Zbl 0319.60053)