Geodesic
CABARET difference scheme with improved dispersion properties
Matematičeskoe modelirovanie, Tome 31 (2019) no. 3, pp. 83-96

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Difference scheme for the advection transport equation has been constructed as the linear combination of "cabaret" scheme and the scheme with the central differences. The research of stability and dispersion properties of the scheme is conducted. It is shown that the constructed scheme has the best dispersion properties for high harmonicas in case of small numbers of Courant in comparison with the known scheme of "cabaret" for advection transport equation. Comparison of errors of this scheme and two-parameter difference scheme of the third order of accuracy on the basis of numerical experiments on sets of test tasks used earlier is carried out. It has been showed, that developed scheme has smaller errors in grid space $L_1$ in comparison of mentioned above scheme. Additionally the developed scheme uses more compact set of nodes (when calculating $i$-go of knot values of the hubs $i-1$, $i$, $i+1$ are used), and requires smaller number of arithmetic operations.
Mots-clés : advection transport problem, “cabaret” scheme
Keywords: dispersion of schemes, accuracy. 
@article{MM_2019_31_3_a5,
     author = {A. I. Sukhinov and A. E. Chistyakov},
     title = {CABARET difference scheme with improved dispersion properties},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {83--96},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2019_31_3_a5/}
}
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A. I. Sukhinov; A. E. Chistyakov. CABARET difference scheme with improved dispersion properties. Matematičeskoe modelirovanie, Tome 31 (2019) no. 3, pp. 83-96. http://geodesic.mathdoc.fr/item/MM_2019_31_3_a5/