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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 7, Pages 1186–1193
DOI: https://doi.org/10.7868/S0044466914040036 (Mi zvmmf10066) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Stable difference schemes for certain parabolic equations

N. M. Afanas'evaa, P. N. Vabishchevichb

a North-Eastern Federal University, ul. Belinskogo 58, Yakutsk, 677000, Russia
b Nuclear Safety Institute, Russian Academy of Sciences, Bol’shaya Tul’skaya ul. 52, Moscow, 115191, Russia
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DOI: https://doi.org/10.7868/S0044466914040036
Abstract: In some applications, boundary value problems for second-order parabolic equations with a special nonself-adjoint operator have to be solved approximately. The operator of such a problem is a weighted sum of self-adjoint elliptic operators. Unconditionally stable two-level schemes are constructed taking into account that the operator of the problem is not self-adjoint. The possibilities of using explicit-implicit approximations in time and introducing a new sought variable are discussed. Splitting schemes are constructed whose numerical implementation involves the solution of auxiliary problems with self-adjoint operators.
Key words: Cauchy problem, second-order parabolic equation, convection-diffusion equation, operator-difference schemes, splitting schemes.
Received: 14.10.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 7, Pages 1159–1166
DOI: https://doi.org/10.1134/S0965542514040034
Bibliographic databases:
Document Type: Article
UDC: 519.693
MSC: 35K40,35K57,65M06
Language: Russian
Citation: N. M. Afanas'eva, P. N. Vabishchevich, “Stable difference schemes for certain parabolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:7 (2014), 1186–1193; Comput. Math. Math. Phys., 54:7 (2014), 1159–1166
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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