Geodesic
Regularized additive operator-difference schemes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 449-457 
P. N. Vabishchevich. Regularized additive operator-difference schemes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 3, pp. 449-457. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a4/
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     author = {P. N. Vabishchevich},
     title = {Regularized additive operator-difference schemes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {449--457},
     year = {2010},
     volume = {50},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_3_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The construction of additive operator-difference (splitting) schemes for the approximate solution Cauchy problem for the first-order evolutionary equation is considered. Unconditionally stable additive schemes are constructed on the basis of the Samarskii regularization principle for operator-difference schemes. In the case of arbitrary multicomponent splitting, these schemes belong to the class of additive full approximation schemes. Regularized additive operator-difference schemes for evolutionary problems are constructed without the assumption that the regularizing operator and the operator of the problem are commutable. Regularized additive schemes with double multiplicative perturbation of the additive terms of the problem’s operator are proposed. The possibility of using factorized multicomponent splitting schemes, which can be used for the approximate solution of steadystate problems (finite difference relaxation schemes) are discussed. Some possibilities of extending the proposed regularized additive schemes to other problems are considered.

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