Power series analysis as a major breakthrough to improve the efficiency of Asymptotic Numerical Method in the vicinity of bifurcations

Abstract : This paper presents the outcome of power series analysis in the framework of the Asymptotic Numerical Method. We theoretically demonstrate and numerically evidence that the emergence of geometric power series in the vicinity of simple bifurcation points is a generic behavior. So we propose to use this hallmark as a bifurcation indicator to locate and compute very efficiently any simple bifurcation point. Finally, a power series that recovers an optimal step length is build in the neighborhood of bifurcation points. The reliability and robustness of this powerful approach is then demonstrated on two application examples from structural mechanics and hydrodynamics
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https://hal.archives-ouvertes.fr/hal-00707513
Contributeur : Bruno Cochelin <>
Soumis le : mardi 12 juin 2012 - 18:18:24
Dernière modification le : vendredi 1 février 2019 - 14:38:40
Document(s) archivé(s) le : jeudi 13 septembre 2012 - 02:35:56

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manbif_12-06-2012.pdf
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  • HAL Id : hal-00707513, version 1

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Bruno Cochelin, Médale Marc. Power series analysis as a major breakthrough to improve the efficiency of Asymptotic Numerical Method in the vicinity of bifurcations. 2012. 〈hal-00707513〉

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