Geodesic
A~variation approach to the construction of finite-difference scheme with space-split time derivative for the Korteweg-de~Vries equation
Matematičeskoe modelirovanie, Tome 12 (2000) no. 4, pp. 105-116.

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The paper presents a variation approach to the construction of finite-difference schemes with space split time derivative (“Cabaret”) for the Korteweg-de Vries (KDV) equation. The test results under different initial distributions are demonstrated. In particular, it is shown that “Cabaret” enjoys the advantage of accurate solution propagation on non-uniform grids over the classical three-layer central differencing (“Cross”). 
@article{MM_2000_12_4_a7,
     author = {V. M. Goloviznin and S. A. Karabasov and D. A. Sykhodulov},
     title = {A~variation approach to the construction of finite-difference scheme with space-split time derivative for the {Korteweg-de~Vries} equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {105--116},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2000_12_4_a7/}
}
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V. M. Goloviznin; S. A. Karabasov; D. A. Sykhodulov. A~variation approach to the construction of finite-difference scheme with space-split time derivative for the Korteweg-de~Vries equation. Matematičeskoe modelirovanie, Tome 12 (2000) no. 4, pp. 105-116. http://geodesic.mathdoc.fr/item/MM_2000_12_4_a7/