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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 7, Pages 1186–1193 (Mi zvmmf10066)  

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, Bolshaya Tulskaya ul. 52, Moscow, 115191, Russia

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.

DOI: https://doi.org/10.7868/S0044466914040036

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:7, 1159–1166

Bibliographic databases:

UDC: 519.693
MSC: 35K40,35K57,65M06
Received: 14.10.2013

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

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