Geodesic
Stable difference schemes for certain parabolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 7, pp. 1186-1193 
N. M. Afanas'eva; P. N. Vabishchevich. Stable difference schemes for certain parabolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 7, pp. 1186-1193. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_7_a7/
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     title = {Stable difference schemes for certain parabolic equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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