Geodesic
A higher-order difference scheme of the Cabaret class for solving the transport equation
Numerical methods and programming, Tome 19 (2018) no. 2, pp. 185-193

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A new difference scheme of the Cabaret class with a higher order of accuracy for solving the scalar transport equation is proposed. The order of approximation of this difference scheme is equal to four. The balance-characteristic representation of the scheme is constructed and the dispersion properties are given. For the proposed difference scheme, a number of examples to solve the transport equation for smooth and discontinuous profiles are considered in comparison with the classical Cabaret scheme.
Mots-clés : Cabaret scheme, transport equation
Keywords: higher order approximation, accuracy. 
@article{VMP_2018_19_2_a6,
     author = {A. V. Solov'ev and A. V. Danilin},
     title = {A higher-order difference scheme of the {Cabaret} class for solving the transport equation},
     journal = {Numerical methods and programming},
     pages = {185--193},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2018_19_2_a6/}
}
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A. V. Solov'ev; A. V. Danilin. A higher-order difference scheme of the Cabaret class for solving the transport equation. Numerical methods and programming, Tome 19 (2018) no. 2, pp. 185-193. http://geodesic.mathdoc.fr/item/VMP_2018_19_2_a6/