Methods of Accelerated Convergence in Nonlinear Mechanics - Couverture souple

Bogoljubov, N.N. N.; Mitropoliskii, J.A.; Samoilenko, A.M.

Couverture souple

ISBN 10 : 3642619029 ISBN 13 : 9783642619021

Editeur : Springer, 2011

Synopsis

This monograph deals with some of the latest results in nonlinear mechanics, obtained recently by the use of a modernized version of Bogoljubov's method of successive changes of variables which ensures rapid convergence. This method visualised as early as 1934 by Krylov and Bogoljubov provides an effective tool for solving many interesting problems of nonlinear mechanics. It led, in particular, to the solution of the problem of the existence of a quasi- periodic regime, with the restriction that approximate solutions obtained in the general case involved divergent series. Recently, making use of the research of Kolmogorov and Arno'ld, Bogoljubov has modernised the method of successive substitutions in such a way that the convergence of the corresponding expansions is ensured. This book consists of a short Introduction and seven chapters. The first chapter presents the results obtained by BogoIjubov in 1963 on the extension of the method of successive substitutions and the study of quasi- periodic solutions applied to non-conservative systems (inter alia making explicit the dependence of these solutions on the parameter, indicating methods of obtaining asymptotic and convergent series for them, etc.).

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2011
• Langue: anglais
• ISBN 10: 3642619029
• ISBN 13: 9783642619021
• Reliure: Broché
• Nombre de pages: 300
• Éditeur: Sneddon I.N.
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne