Convergence and Accuracy of the Method of Iterative Approximate Factorization of Operators in Multidimensional High-Accuracy Bicompact Schemes

The convergence and accuracy of a method for solving high-order accurate bicompact schemes having the fourth order of approximation in spatial variables on a minimum stencil for a multidimensional inhomogeneous advection equation are investigated. The method is based on the approximate factorization...

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Bibliographic Details
Published in:Mathematical models and computer simulations 2020-09, Vol.12 (5), p.660-675
Main Authors: Rogov, B. V., Chikitkin, A. V.
Format: Article
Language:English
Subjects:
Accuracy
Advection
Algorithms
Approximation
Convergence
Factorization
Finite differences
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Simulation and Modeling
Spatial marching
Spectral methods
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Summary:The convergence and accuracy of a method for solving high-order accurate bicompact schemes having the fourth order of approximation in spatial variables on a 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 the second) order of accuracy of bicompact schemes in time. The convergence of these iterations for both two- and three-dimensional bicompact schemes as applied to the linear inhomogeneous advection equation with positive constant coefficients is proved using the spectral method. The efficiency of two parallel algorithms for solving equations of multidimensional bicompact schemes is compared. One of them is the spatial marching algorithm for calculating unfactorized schemes, and the other is based on iterative approximate factorization of difference operators of the schemes.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048220050178