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Sur laB-stabilité des méthodes de Runge-Kutta

OnB-stability of the methods of Runge Kutta

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Summary

In this paper, we slightly modify the definition ofB-stability of Butcher [1], so as to cover a wider class of differential equations, and we give simple characterizations of this property.

Résumé

Dans cet article, nous modifions légèrement la définition de laB-stabilité donnée par J.C. Butcher [1] afin qu'elle s'applique à une plus large classe d'équations différentielles et nous donnons des caractérisations simples de cette propriété.

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Bibliographie

  1. Butcher, J.C.: A stability property of implicit Runge-Kutta methods. Nordisk Tidskr. Informationsbehandling (BIT)15, 358–361 (1975)

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  3. Chipman, F.H.: A-stable Runge-Kutta processes. Nordisk Tidskr. Informationsbehandling (BIT)11, 384–388 (1971)

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  4. Crouzeix, M.: Sur l'approximation des equations differentielles opérationnelles linéaires par des méthodes de Runge-Kutta. Thèse, Paris, 1975

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Crouzeix, M. Sur laB-stabilité des méthodes de Runge-Kutta. Numer. Math. 32, 75–82 (1979). https://doi.org/10.1007/BF01397651

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  • DOI: https://doi.org/10.1007/BF01397651

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