Methods of Accelerated Convergence in Nonlinear Mechanics - Tapa blanda

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

 
9783642619021: Methods of Accelerated Convergence in Nonlinear Mechanics
Tapa blanda
ISBN 10: 3642619029 ISBN 13: 9783642619021
Editorial: Springer, 2011

Sinopsis

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.).

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Reseña del editor

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.).

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Editorial
Springer
Año de publicación
2011
Idioma
Inglés
ISBN 10 
3642619029
ISBN 13 
9783642619021
Encuadernación
Tapa blanda
Número de páginas
300
Editor
Sneddon I.N.
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Alemania

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