Geodesic
Construction of third-order schemes using Lagrange-Burmann expansions for the numerical integration of inviscid gas equations
Numerical methods and programming, Tome 17 (2016) no. 1, pp. 21-43.

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It is proposed to construct several explicit third-order difference schemes for the hyperbolic conservation laws using the expansions of grid functions in Lagrange–Burmann series. The results of test computations for the one-dimensional advection equation and multidimensional Euler equations governing the inviscid compressible gas flows confirm the third order of accuracy of the constructed schemes. The quasi-monotonous profiles of numerical solutions are obtained.
Keywords: hyperbolic conservation laws, Lagrange–Burmann expansions, difference methods. 
@article{VMP_2016_17_1_a3,
     author = {E. V. Vorozhtsov},
     title = {Construction of third-order schemes using {Lagrange-Burmann} expansions for the numerical integration of inviscid gas equations},
     journal = {Numerical methods and programming},
     pages = {21--43},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a3/}
}
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E. V. Vorozhtsov. Construction of third-order schemes using Lagrange-Burmann expansions for the numerical integration of inviscid gas equations. Numerical methods and programming, Tome 17 (2016) no. 1, pp. 21-43. http://geodesic.mathdoc.fr/item/VMP_2016_17_1_a3/