Geodesic
Local Parameterization and the Asymptotic Numerical Method
H. Mottaqui1 ; B. Braikat1 ; N. Damil1
1 Laboratory of Computing Science in Mechanic, Faculty of Science Ben M’Sik University of Hassan II Mohammedia - Casablanca, B.P. 7955 Sidi Othmane, Casablanca, Morocco
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 16-22.

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The Asymptotic Numerical Method (ANM) is a family of algorithms, based on computation of truncated vectorial series, for path following problems [2]. In this paper, we present and discuss some techniques to define local parameterization [4, 6, 7] in the ANM. We give some numerical comparisons of pseudo arc-length parameterization and local parameterization on non-linear elastic shells problems
DOI : 10.1051/mmnp/20105703

H. Mottaqui 1 ; B. Braikat 1 ; N. Damil 1

1 Laboratory of Computing Science in Mechanic, Faculty of Science Ben M’Sik University of Hassan II Mohammedia - Casablanca, B.P. 7955 Sidi Othmane, Casablanca, Morocco 
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H. Mottaqui; B. Braikat; N. Damil. Local Parameterization and the Asymptotic Numerical Method. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 7 Supplement, pp. 16-22. doi : 10.1051/mmnp/20105703. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20105703/

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[4] J. J. Gervais, H. Sadiky A new steplength control for continuation with the asymptotic numerical method IAM, J. Nomer. Anal. 2000 207 229

[5] H. Mottaqui, B. Braikat, N. Damil.Influence de la paramétrisation dans la méthode asymptotique numérique : Application au calcul de structures. Premier congrès Tunisien de mécanique, (2008), 173–174.

[6] W. C. Rheinboldt, J. V. Burkadt A Localy parameterized continuation Acm Transaction on Mathmatical Software 1983 215 235

[7] R. Seydel. World of bifurcation, online collection and tutorials of nonlinear phenomena, (www.bifurcation.de) (1999).

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