Approximation Procedures in Nonlinear Oscillation Theory

✍ Scribed by Nikolai A. Bobylev; Yurii M. Burman; Sergey K. Korovin

• Publisher: De Gruyter
• Year: 1994
• Tongue: English
• Leaves: 284
• Series: De Gruyter Series in Nonlinear Analysis and Applications; 2
• Edition: Reprint 2012
• Category: Library

✦ Synopsis

"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 für Mathematik

✦ Table of Contents

Preface
Chapter I: Basic Concepts
§ 1 Equations for oscillatory systems
§ 2 The shift operator and first return function
§ 3 Integral and integrofunctional operators for periodic problem
§ 4 The harmonic balance method
§ 5 The method of mechanical quadratures
§ 6 The collocation method
§ 7 The method of finite differences
§ 8 Factor methods
Chapter II: Existence theorems for oscillatory regimes
§ 1 Smooth manifolds and differential forms
§ 2 Degree of a mapping
§ 3 Rotation of vector fields
§ 4 Completely continuous vector fields
§ 5 Fixed point principles and solution of operator equations
§ 6 Forced oscillations in systems with weak nonlinearities
§ 7 Oscillations in systems with strong nonlinearities. Directing functions method
Chapter III: Convergence of numerical procedures
§ 1 Projection methods
§ 2 Factor methods
§ 3 Convergence of the harmonic balance method and the collocation method in the problem of periodic oscillations
§ 4 Convergence of the method of mechanical quadratures
§ 5 Convergence of the method of finite differences
§ 6 Numerical procedures of approximate construction of oscillatory regimes in autonomous systems
§ 7 Affinity theory
§ 8 Effective convergence criteria for numerical procedures
§ 9 Effective estimates of the convergence rate for the harmonic balance method
Notes on the References
References
Index