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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 2, Pages 253–262 (Mi zvmmf9655)  

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

Construction of splitting schemes based on transition operator approximation

P. N. Vabishchevich

Nuclear Safety Institute, Russian Academy of Sciences, BolТshaya TulТskaya ul. 52, Moscow, 115191 Russia

Abstract: The stability analysis of approximate solutions to unsteady problems for partial differential equations is usually based on the use of the canonical form of operator-difference schemes. Another possibility widely used in the analysis of methods for solving Cauchy problems for systems of ordinary differential equations is associated with the estimation of the norm of the transition operator from the current time level to a new one. The stability of operator-difference schemes for a first-order model operator-differential equation is discussed. Primary attention is given to the construction of additive schemes (splitting schemes) based on approximations of the transition operator. Specifically, classical factorized schemes, componentwise splitting schemes, and regularized operator-difference schemes are related to the use of a certain multiplicative transition operator. Additive averaged operator-difference schemes are based on an additive representation of the transition operator. The construction of second-order splitting schemes in time is discussed. Inhomogeneous additive operator-difference schemes are constructed in which various types of transition operators are used for individual splitting operators.

Key words: Cauchy problem, first-order evolution equation, operator-difference schemes, splitting schemes

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:2, 235–244

Bibliographic databases:

UDC: 519.63
Received: 14.06.2011

Citation: P. N. Vabishchevich, “Construction of splitting schemes based on transition operator approximation”, Zh. Vychisl. Mat. Mat. Fiz., 52:2 (2012), 253–262; Comput. Math. Math. Phys., 52:2 (2012), 235–244

Citation in format AMSBIB
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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. P. N. Vabishchevich, “Flux-splitting schemes for parabolic problems”, Comput. Math. Math. Phys., 52:8 (2012), 1128–1138  mathnet  crossref  mathscinet  isi  elib  elib
    2. Comput. Math. Math. Phys., 53:7 (2013), 1013–1025  mathnet  crossref  crossref  isi  elib  elib
    3. P. N. Vabishchevich, “Flux-splitting schemes for parabolic equations with mixed derivatives”, Comput. Math. Math. Phys., 53:8 (2013), 1139–1152  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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