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Stable Runge-Kutta integrations for differential systems with semi-stable equilibria

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Summary.

In this paper, the stability of Runge-Kutta methods for differential systems with semi-stable equilibria is analyzed. In fact, a way of circumventing the very severe ‘‘unconditional stability barrier’’ [3] is proposed. The usage of time-meshes with step-size ratios under some constant greater than one, as usual in standard numerical codes, is considered in order to recover stability for many implicit methods. The main result roughly says that any ‘‘strongly’’ A-stable Runge-Kutta method is stable for this kind of differential systems on this sort of meshes.

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Authors and Affiliations

  1. Dpto. de Análisis Matemático, Universidad de La Laguna, 38200, La Laguna, Tenerife, Canary Islands, Spain

    S. González-Pinto & D. Hernández-Abreu

Authors
  1. S. González-Pinto
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  2. D. Hernández-Abreu
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Correspondence to S. González-Pinto.

Additional information

Work supported by project BMF2001-2562

Mathematical Subject Classifications (2000): 65L20

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González-Pinto, S., Hernández-Abreu, D. Stable Runge-Kutta integrations for differential systems with semi-stable equilibria. Numer. Math. 97, 473–491 (2004). https://doi.org/10.1007/s00211-003-0513-6

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  • DOI: https://doi.org/10.1007/s00211-003-0513-6

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