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Found 133 Documents (Results 1–100)

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
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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).
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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
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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).
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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).
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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
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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).
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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
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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
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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
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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
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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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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).
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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).
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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).
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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
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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
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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).
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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
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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
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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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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
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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).
MSC:  65M06 35B25 35K20
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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).
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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
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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).
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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).
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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).
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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).
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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).
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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)
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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).
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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).
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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).
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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)
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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).
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