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 Matem. Mod., 2019, Volume 31, Number 12, Pages 119–144 (Mi mm4143)

About the convergence and accuracy of the method of iterative approximate factorization of operators of multidimensional high-accuracy bicompact schemes

B. V. Rogova, A. V. Chikitkinb

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology, Dolgoprudny

Abstract: In the work, the convergence and accuracy of the method of solving high-precision bicompact schemes having the fourth order of approximation in spatial variables on the minimum stencil for a multidimensional inhomogeneous advection equation are investigated. The method is based on the approximate factorization of difference operators of multidimensional bicompact schemes. In addition, it uses iterations to preserve a high (higher than second) order of accuracy of bicompact schemes in time. Using the spectral method, we were able to prove the convergence of these iterations for both twodimensional and three-dimensional bicompact schemes for a linear inhomogeneous advection equation with constant positive coefficients. The effectiveness of two parallel algorithms for solving multidimensional bicompact schemes equations is compared. The first of them is the spatial marching algorithm for calculation of non-factorized schemes, and the second is based on an iterative approximate factorization of difference operators of the schemes.

Keywords: multidimensional inhomogeneous advection equation, bicompact schemes, parallel algorithms, iterative approximate factorization method.

DOI: https://doi.org/10.1134/S0234087919120098

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Revised: 26.09.2019
Accepted:21.10.2019

Citation: B. V. Rogov, A. V. Chikitkin, “About the convergence and accuracy of the method of iterative approximate factorization of operators of multidimensional high-accuracy bicompact schemes”, Matem. Mod., 31:12 (2019), 119–144

Citation in format AMSBIB
\Bibitem{RogChi19} \by B.~V.~Rogov, A.~V.~Chikitkin \paper About the convergence and accuracy of the method of iterative approximate factorization of operators of multidimensional high-accuracy bicompact schemes \jour Matem. Mod. \yr 2019 \vol 31 \issue 12 \pages 119--144 \mathnet{http://mi.mathnet.ru/mm4143} \crossref{https://doi.org/10.1134/S0234087919120098} \elib{https://elibrary.ru/item.asp?id=41298293} 

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This publication is cited in the following articles:
1. E. N. Aristova, G. O. Astafurov, “O sravnenii dissipativno-dispersionnykh svoistv nekotorykh konservativnykh raznostnykh skhem”, Preprinty IPM im. M. V. Keldysha, 2020, 117, 22 pp.
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