Méthode Asymptotique Numérique (in french) by B. Cochelin, N. Damil and M. Potier-Ferry. Hermes Sciences, Lavoisier 2007.


L. Guillot, A. Lazarus, O. Thomas, C. Vergez, B. Cochelin "A purely frequency based Floquet-Hill formulation for the efficient stability computation of periodic solutions of ordinary differential systems", Journal of Computational Physics, vol. 416, 2020.

L. Guillot, B. Cochelin, C. Vergez "A Taylor series-based continuation method for solutions of dynamical systems", Nonlinear Dynamics, p. 1-19, 2019.

L. Guillot, C. Vergez, B. Cochelin "Continuation of periodic solutions of various types of delay differential equations using asymptotic numerical method and harmonic balance method", Nonlinear Dynamics, vol. 97(1), p. 123-134, 2019.

L. Guillot, B. Cochelin, C. Vergez "A generic and efficient Taylor series–based continuation method using a quadratic recast of smooth nonlinear systems", International Journal of Numerical Methods in Engineering, vol. 119(4), p. 261-280, 2019.

L. Guillot, P. Vigué, C. Vergez, B. Cochelin "Continuation of quasi-periodic solutions with two-frequency Harmonic Balance Method", Journal of Sound and Vibration, vol. 394, p. 434-450, 2017.

P. Vigué, C. Vergez, S. Karkar, B. Cochelin "Regularized friction and continuation: Comparison with Coulomb’s law", vol. 389, p.350-363, 2017.

S. Karkar, B. Cochelin, C. Vergez "A comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems", Journal of Sound and Vibration, vol. 333, num. 12, p. 2554-2567, 2014.

B.Cochelin, M. Medale "Power series analysis as a major breakthrough to improve the efficiency of Asymptotic Numerical Method in the vicinity of bifurcations." Journal of Computational Physics vol. 236, p. 594-607, 2013.- (download HAL version).

S. Karkar, B. Cochelin, C. Vergez "A high-order, purely frequency based harmonic balance formulation for continuation of periodic solutions: The case of non-polynomial nonlinearities", Journal of Sound and Vibration vol. 332, num. 4, pp. 968-977, 2013.

O. Thomas, A. Lazarus and C. Touzé "A harmonic-based method for computing the stability of periodic oscillations of non-linear structural systems", Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2010, August 2010, Montreal, Canada.

A. Lazarus and O. Thomas "A harmonic-based method for computing the stability of periodic solutions of dynamical systems", Comptes Rendus Mécanique, 338(9), pp. 510-517, 2010.

B. Cochelin C. Vergez. "A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions", Journal of Sound and Vibration, 2009.(download HAL version).

S. Baguet B. Cochelin. ’’ On the behaviour of the ANM continuation in the presence of bifurcations’’, Comm. In Numer. Meth. in Engng,Vol 19, N° 6, p459-471, 2003.

J.M. Cadou, M. Potier-Ferry, B. Cochelin and N. Damil "Asymptotic Numerical Method for stationary Navier-Stokes equation and with Petrov-Galerkin formulation", Int. J. Numer. Methods Engng, Vol 50, p 825-845, 2001

H. Zarouni, B. Cochelin and M. Potier-Ferry. "Asymptotic-numerical methods for shells with finite rotations" Computer Methods in Applied Mecahnics and Engineering, Vol 175, 71-85, 1999.

A. Najah, B. Cochelin, N. Damil and M. Potier-Ferry. "A critical review of Asymptotic-Numerical Method"" Archives of Computational Methods in Engineering, Vol 5, 31-50, 1998

B. Cochelin. " A path following technique via an Asymptotic-Numerical method" Computers & Structures, Vol 53, N° 5, p 1181-1192, 1994.

B. Cochelin, N. Damil and M. Potier-Ferry. " Asymptotic-Numerical Methods and Padé approximants for non- linear elastic structures" Int. J. Numer. Methods Engng , Vol 37, p 1187-1213, 1994.

PhD. Theses

L. Guillot "On a quadratic formalism for the continuation of the solutions of dynamical systems and their bifurcations - Applications to reed instruments", PhD Thesis, Aix-Marseille University, 2020 (supervisors : C.Vergez and B.Cochelin)

Below, a package containing the articles (author’s versions) from the PhD Thesis to download :

Zip - 11 Mb
Papers from L.Guillot PhD

P. Vigué "Solutions périodiques et quasi-périodiques de systèmes dynamiques d’ordre entier ou fractionnaire - Applications à la corde frottée", PhD Thesis, Aix-Marseille University, 2017 (supervisors : C.Vergez and B.Cochelin)

S. Karkar "Méthodes numériques pour les systèmes dynamiques non linéaires. Application aux instruments de musique auto-oscillants", PhD Thesis, Aix-Marseille University, 2012. (supervisors : B. Cochelin and C. Vergez)