AGROCAMPUS OUEST (Institut Supérieur des Sciences Agronomiques, Agroalimentaires, Horticoles et du Paysage - 65, rue de St Brieuc - CS 84215 - 35042 Rennes cedex - France)
3Konputazio Zientziak eta A.A. Saila [Spain] (Universidad del Pais Vasco Konputazio Zientziak eta A.A. Saila Informatika Fakultatea, UPV/EHU 20018 Donostia-San Sebastián - Espagne)
UPV/EHU - Universidad del Pais Vasco / Euskal Herriko Unibertsitatea [Espagne] (Barrio Sarriena s/n, 48940 Leioa, Bizkaia
Campus d'Álava : Vice-Rectorado, San Antonio 41, 01005 Vitoria ;
campus de Biscaye et services centraux : Apdo 1397, 48080 Bilbao ;
campus de Guipúzcoa : Vice-Rectorado, Fuenterrabia 13-1° , 20006 San Sebastián - Espagne)
Abstract : The stroboscopic averaging method (SAM) is a technique for the integration of highly oscillatory differential systems dy/dt = f(y; t) with a single high frequency. The method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averaging which constructs an averaged differential system dY/dt = F(Y ) whose solutions Y interpolate the sought highly oscillatory solutions y. SAM integrates numerically the averaged system without using the analytic expression of F; all information on F required by the algorithm is gathered on the fly by numerically integrating the originally given system in small time windows. SAM may be easily implemented in combination with standard software and may be applied with variable step sizes. Furthermore it may also be used successfully to integrate oscillatory DAEs. The paper provides an analytic and experimental study of SAM and two related techniques: the LISP algorithms of Kirchgraber and multirevolution methods.
https://hal.inria.fr/hal-00777181
Contributeur : Philippe Chartier
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Soumis le : jeudi 24 janvier 2013 - 11:40:56
Dernière modification le : jeudi 15 novembre 2018 - 11:57:05
Document(s) archivé(s) le : jeudi 25 avril 2013 - 03:51:06
Maripaz Calvo, Philippe Chartier, Ander Murua, Jesus Maria Sanz-Serna. Numerical stroboscopic averaging for ODEs and DAEs. Applied Numerical Mathematics, Elsevier, 2011, 61 (10), pp.1077-1095. 〈10.1016/j.apnum.2011.06.007〉. 〈hal-00777181〉
