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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 3, Pages 449–457 (Mi zvmmf4842)  

This article is cited in 3 scientific papers (total in 3 papers)

Regularized additive operator-difference schemes

P. N. Vabishchevich

Institute of Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moskow, 125047 Russia

Abstract: 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.

Key words: first-order evolutionary equation, operator-difference schemes, stability, additive schemes, regularization of finite difference schemes.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:3, 428–436

Bibliographic databases:

UDC: 519.63
Received: 16.07.2009

Citation: P. N. Vabishchevich, “Regularized additive operator-difference schemes”, Zh. Vychisl. Mat. Mat. Fiz., 50:3 (2010), 449–457; Comput. Math. Math. Phys., 50:3 (2010), 428–436

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Vabishchevich P.N., “On a new class of additive (splitting) operator-difference schemes”, Math. Comp., 81:277 (2012), 267–276  crossref  mathscinet  zmath  isi  scopus
    2. M. Kh. Shkhanukov-Lafishev, S. M. Arkhestova, M. B. Tkhamokov, “Vektornye additivnye skhemy dlya nekotorykh klassov uravnenii giperbolicheskogo tipa”, Vladikavk. matem. zhurn., 15:1 (2013), 71–84  mathnet
    3. Vabishchevich P.N. Grigor'ev A.V., “Splitting Schemes for Pseudoparabolic Equations”, Differ. Equ., 49:7 (2013), 807–814  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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