Geodesic
On monotony of balance-characteristic scheme
Matematičeskoe modelirovanie, Tome 21 (2009) no. 7, pp. 29-42.

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The necessary and sufficient conditions are obtained for difference initial date provided a monotony of balance-characteristic scheme on initial time half-step. It was shown that on elemental time step the scheme is monotone at Curant number $r\in(0,0.5]$ and nonmonotone at $r\in(0.5,1)$ in the case of standard nonlinear correction of flux variables. It was proposed a method provided a monotony of balance-characteristic scheme at Curant number $r\in(0,1]$ at whish the scheme is stable. The binary correction of flux variables lies in the base of the method, it allows conserve the compactness of scheme space stencil. Results of test calculations are presented to demonstrate the advantage of modified scheme. 
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V. V. Ostapenko. On monotony of balance-characteristic scheme. Matematičeskoe modelirovanie, Tome 21 (2009) no. 7, pp. 29-42. http://geodesic.mathdoc.fr/item/MM_2009_21_7_a2/

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