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Approximation Procedures in Nonlinear Oscillation Theory : Contributions to the Sociology of Language - Nikolai A. Bobylov

Approximation Procedures in Nonlinear Oscillation Theory

Contributions to the Sociology of Language

Hardcover Published: 1994
ISBN: 9783110141320
Number Of Pages: 283
For Ages: 22+ years old

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The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jurgen Appell."

Industry Reviews

"The book is well written and provides a good view of the important contributions of the school of Krasnoselʹskiĭ in the theory of nonlinear oscillations." Mathematical Reviews

"Undoubtedly it [the book] will be useful to all specialists in nonlinear analysis as well as oscillation theory." Zentralblatt fur Mathematik

Basic Conceptsp. 1
Equations for oscillatory systemsp. 1
The shift operator and first return functionp. 8
Integral and integrofunctional operators for periodic problemp. 11
The harmonic balance methodp. 20
The method of mechanical quadraturesp. 25
The collocation methodp. 29
The method of finite differencesp. 33
Factor methodsp. 37
Existence theorems for oscillatory regimesp. 43
Smooth manifolds and differential formsp. 43
Degree of a mappingp. 51
Rotation of vector fieldsp. 65
Completely continuous vector fieldsp. 73
Fixed point principles and solution of operator equationsp. 80
Forced oscillations in systems with weak nonlinearitiesp. 94
Oscillations in systems with strong nonlinearities. Directing functions methodp. 98
Convergence of numerical proceduresp. 107
Projection methodsp. 107
Factor methodsp. 119
Convergence of the harmonic balance method and the collocation method in the problem of periodic oscillationsp. 148
Convergence of the method of mechanical quadraturesp. 171
Convergence of the method of finite differencesp. 188
Numerical procedures of approximate construction of oscillatory regimes in autonomous systemsp. 198
Affinity theoryp. 215
Effective convergence criteria for numerical proceduresp. 235
Effective estimates of the convergence rate for the harmonic balance methodp. 240
Notes on the Referencesp. 251
Referencesp. 257
Indexp. 271
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783110141320
ISBN-10: 3110141329
Series: Contributions to the Sociology of Language
Audience: General
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 283
Published: 1994
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99  x 1.75
Weight (kg): 0.65