
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, Bol’shaya Tul’skaya 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 operatordifference 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 operatordifference schemes for a firstorder model operatordifferential 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 operatordifference schemes are related to the use of a certain multiplicative transition operator. Additive averaged operatordifference schemes are based on an additive representation of the transition operator. The construction of secondorder splitting schemes in time is discussed. Inhomogeneous additive operatordifference schemes are constructed in which various types of transition operators are used for individual splitting operators.
Key words:
Cauchy problem, firstorder evolution equation, operatordifference schemes, splitting schemes
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Computational Mathematics and Mathematical Physics, 2012, 52:2, 235–244
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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
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This publication is cited in the following articles:

P. N. Vabishchevich, “Fluxsplitting schemes for parabolic problems”, Comput. Math. Math. Phys., 52:8 (2012), 1128–1138

Comput. Math. Math. Phys., 53:7 (2013), 1013–1025

P. N. Vabishchevich, “Fluxsplitting schemes for parabolic equations with mixed derivatives”, Comput. Math. Math. Phys., 53:8 (2013), 1139–1152

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