Stability and accuracy for implicit semidiscretizations of hyperbolic problems |
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Authors: | Klaus-Günther Strack |
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Affiliation: | (1) Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, D-5100 Aachen, Federal Republic of Germany |
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Abstract: | Summary In this paper we give bounds for the error constants of certain classes of stable implicit finite difference methods for first order hyperbolic equations in one space dimension. We consider classes of methods that user downwind ands upwind points in the explicit part andR downwind andS upwind points in the implicit part, respectively, and that are of optimal orderp=min (r+R+s+S, 2(r+R+1), 2(s+S)).In some cases the error constant of interpolatory methods [5] can be improved. The results are proved via the order star technique. They are further used to determine methods of optimal order that are stable. |
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Keywords: | AMS (MOS) 65M10 CR: G1.8 |
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