Geodesic
Using the Sharp scheme of higher-order accuracy for solving some nonlinear hyperbolic systems of equations
Numerical methods and programming, Tome 20 (2019) no. 1, pp. 45-53

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The Sharp difference scheme of higher-order accuracy developed previously for solving the scalar one-dimensional transport equation is extended to the shallow water nonlinear systems and to the systems of Euler equations using the balance-characteristic approach. For these systems, a number of test problems are solved to illustrate the features of the solutions obtained by the described difference scheme.
Keywords: Cabaret method, Sharp scheme, hyperbolic equations, high-accuracy schemes. 
@article{VMP_2019_20_1_a4,
     author = {A. V. Solov'ev and A. V. Danilin},
     title = {Using the {Sharp} scheme of higher-order accuracy for solving some nonlinear hyperbolic systems of equations},
     journal = {Numerical methods and programming},
     pages = {45--53},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2019_20_1_a4/}
}
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A. V. Solov'ev; A. V. Danilin. Using the Sharp scheme of higher-order accuracy for solving some nonlinear hyperbolic systems of equations. Numerical methods and programming, Tome 20 (2019) no. 1, pp. 45-53. http://geodesic.mathdoc.fr/item/VMP_2019_20_1_a4/