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 Zh. Vychisl. Mat. Mat. Fiz., 1997, Volume 37, Number 4, Pages 429–446 (Mi zvmmf2084)

Singularly perturbed boundary value problems with concentrated sources and discontinuous initial conditions

G. I. Shishkin

Ekaterinburg

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English version:
Computational Mathematics and Mathematical Physics, 1997, 37:4, 417–434

Bibliographic databases:
UDC: 519.633
MSC: Primary 35K20; Secondary 39A10, 35B25, 65N12, 35R05

Citation: G. I. Shishkin, “Singularly perturbed boundary value problems with concentrated sources and discontinuous initial conditions”, Zh. Vychisl. Mat. Mat. Fiz., 37:4 (1997), 429–446; Comput. Math. Math. Phys., 37:4 (1997), 417–434

Citation in format AMSBIB
\Bibitem{Shi97} \by G.~I.~Shishkin \paper Singularly perturbed boundary value problems with concentrated sources and discontinuous initial conditions \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 1997 \vol 37 \issue 4 \pages 429--446 \mathnet{http://mi.mathnet.ru/zvmmf2084} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1452589} \zmath{https://zbmath.org/?q=an:0940.35104} \transl \jour Comput. Math. Math. Phys. \yr 1997 \vol 37 \issue 4 \pages 417--434 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Braianov I.A., Vulkov L.G., “Grid approximation for the solution of the singularly perturbed heat equation with concentrated capacity”, J Math Anal Appl, 237:2 (1999), 672–697
2. I. A. Brayanov, L. G. Volkov, “Uniform in a small parameter convergence of Samarskii's monotone scheme and its modification for the convection-diffusion equation with a concentrated source”, Comput. Math. Math. Phys., 40:4 (2000), 534–550
3. Braianov I.A., Kandilarov J.D., Vulkov L.G., “Numerical solution of diffusion-desorbtion problems with small diffusion coefficients and localized chemical reactions”, Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems, 2000, 169–176
4. Shishkin G.I., “Grid approximation of parabolic convection-diffusion equations with piecewise smooth initial conditions”, Doklady Mathematics, 72:3 (2005), 850–853
5. G. I. Shishkin, “Grid approximation of singularly perturbed parabolic convection-diffusion equations with a piecewise-smooth initial condition”, Comput. Math. Math. Phys., 46:1 (2006), 49–72
6. Brayanov I.A., “Numerical solution of a mixed singularly perturbed parabolic-elliptic problem”, J Math Anal Appl, 320:1 (2006), 361–380
7. Comput. Math. Math. Phys., 47:3 (2007), 442–462
8. Shishkin G.I., “Grid approximation of singularly perturbed parabolic reaction-diffusion equations with piecewise smooth initial-boundary conditions”, Mathematical Modelling and Analysis, 12:2 (2007), 235–254
9. G. I. Shishkin, “The Richardson scheme for the singularly perturbed parabolic reaction-diffusion equation in the case of a discontinuous initial condition”, Comput. Math. Math. Phys., 49:8 (2009), 1348–1368
10. G. I. Shishkin, “Approximation of singularly perturbed parabolic equations in unbounded domains subject to piecewise smooth boundary conditions in the case of solutions that grow at infinity”, Comput. Math. Math. Phys., 49:10 (2009), 1748–1764
11. Priyadharshini R.M., Ramanujam N., “Approximation of Derivative for a Singularly Perturbed Second-Order ODE of Robin Type with Discontinuous Convection Coefficient and Source Term”, Numerical Mathematics-Theory Methods and Applications, 2:1 (2009), 100–118
12. Shishkin G., “Improved Difference Scheme for a Singularly Perturbed Parabolic Reaction-Diffusion Equation with Discontinuous Initial Condition”, Numerical Analysis and its Applications - 4th International Conference, NAA 2008, Lecture Notes in Computer Science, 5434, 2009, 116–127
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