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
Contributor : Bruno Cochelin <>
Submitted on : Tuesday, June 12, 2012 - 6:18:24 PM
Last modification on : Monday, March 4, 2019 - 2:04:23 PM
Long-term archiving on : Thursday, September 13, 2012 - 2:35:56 AM

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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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