Geodesic
Implicit and time reversible CABARET schemes for quasilinear shallow water equations
Numerical methods and programming, Tome 17 (2016) no. 4, pp. 402-414.

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A new implicit unconditionally stable scheme for the one-dimensional shallow water equations is proposed. This implicit scheme retains all the features of the explicit CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) difference scheme. Dissipative and dispersion properties of this new scheme are analyzed; an algorithm of its numerical solution is discussed. Some examples of solving the Riemann problem are considered.
Mots-clés : CABARET scheme
Keywords: shallow water equations, conservative schemes, time reversible schemes, numerical simulation. 
@article{VMP_2016_17_4_a4,
     author = {V. M. Goloviznin and D. Yu. Gorbachev and A. M. Kolokolnikov and P. A. Maiorov and P. A. Maiorov and B. A. Tlepsuk},
     title = {Implicit and time reversible {CABARET} schemes for quasilinear shallow water equations},
     journal = {Numerical methods and programming},
     pages = {402--414},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2016_17_4_a4/}
}
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V. M. Goloviznin; D. Yu. Gorbachev; A. M. Kolokolnikov; P. A. Maiorov; P. A. Maiorov; B. A. Tlepsuk. Implicit and time reversible CABARET schemes for quasilinear shallow water equations. Numerical methods and programming, Tome 17 (2016) no. 4, pp. 402-414. http://geodesic.mathdoc.fr/item/VMP_2016_17_4_a4/