Geodesic
The optimal explicit unconditionally stable box scheme
Mathematica Applicanda, Tome 26 (1997) no. 40, pp. 31-39.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

The finite difference “box” scheme, (see also [1],[2]), is considered on the simplest possible model of single first order linear hyperbolic equation: ut+mux=0 with constant, coefficient m, and one space variable. The optimal version of the scheme, which is nonoscilating and unconditionally stable with respect to the initial and boundary conditions, is derived in the class of box schemes of the order at, least one. If apropriately iterated, this ścinane may be applied to general systems of quasilinear first order hyperbolic equations in one space variable, as an explicit, unconditionally stable solver. For more than one space variable this solver is applicable via splitting (see [3]).
DOI : 10.14708/ma.v26i40.1857
Classification : 65M06 (65M12)
Mots-clés : Finite difference methods, Stability and convergence of numerical methods 
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Krzysztof Moszyński. The optimal explicit unconditionally stable box scheme. Mathematica Applicanda, Tome 26 (1997) no. 40, pp.  31-39. doi : 10.14708/ma.v26i40.1857. http://geodesic.mathdoc.fr/articles/10.14708/ma.v26i40.1857/

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