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Methods of Accelerated Convergence in Nonlinear Mechanics (Paperback, Softcover reprint of the original 1st ed. 1976)
Loot Price: R1,571
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Methods of Accelerated Convergence in Nonlinear Mechanics (Paperback, Softcover reprint of the original 1st ed. 1976)
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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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