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
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.
Cauchy problem, first-order evolution equation, operator-difference schemes, splitting schemes
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Computational Mathematics and Mathematical Physics, 2012, 52:2, 235–244
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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\paper Construction of splitting schemes based on transition operator approximation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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This publication is cited in the following articles:
P. N. Vabishchevich, “Flux-splitting 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, “Flux-splitting schemes for parabolic equations with mixed derivatives”, Comput. Math. Math. Phys., 53:8 (2013), 1139–1152
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