Approximation Procedures in Nonlinear Oscillation Theory (De Gruyter Series in Nonlinear Analysis & Applications): 2 3110141329, 9783110141320
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear an
129 111 1MB
English Pages 286 [284] Year 1994
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
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
- Author / Uploaded
- N. A. Bobylev
- Nikolai A. Bobylev
- Yuri M. Burman
![Approximation Procedures in Nonlinear Oscillation Theory (De Gruyter Series in Nonlinear Analysis and Applications, 2) [Reprint 2012 ed.]
3110141329, 9783110141320](https://ebin.pub/img/200x200/approximation-procedures-in-nonlinear-oscillation-theory-de-gruyter-series-in-nonlinear-analysis-and-applications-2-reprint-2012nbsped-3110141329-9783110141320.jpg)
![Approximation Procedures in Nonlinear Oscillation Theory [Reprint 2012 ed.]
9783110885712, 9783110141320](https://ebin.pub/img/200x200/approximation-procedures-in-nonlinear-oscillation-theory-reprint-2012nbsped-9783110885712-9783110141320.jpg)
![Lie Group Analysis of Differential Equations: Invariant Solutions of Nonlinear Physical Phenomena (De Gruyter Series in Nonlinear Analysis and Applications, 43) [1 ed.]
3111386996, 9783111386997](https://ebin.pub/img/200x200/lie-group-analysis-of-differential-equations-invariant-solutions-of-nonlinear-physical-phenomena-de-gruyter-series-in-nonlinear-analysis-and-applications-43-1nbsped-3111386996-9783111386997.jpg)
![Nonlinear Time Series Analysis in the Geosciences: Applications in Climatology, Geodynamics and Solar-Terrestrial Physics [proof]](https://ebin.pub/img/200x200/nonlinear-time-series-analysis-in-the-geosciences-applications-in-climatology-geodynamics-and-solar-terrestrial-physics-proof.jpg)
![Nonlinear Time Series Analysis [2 ed.]
0521821509, 9780521821506](https://ebin.pub/img/200x200/nonlinear-time-series-analysis-2nbsped-0521821509-9780521821506.jpg)
![Nonlinear Dynamics (De Gruyter Textbook) [1 ed.]
3110677865, 9783110677867](https://ebin.pub/img/200x200/nonlinear-dynamics-de-gruyter-textbook-1nbsped-3110677865-9783110677867.jpg)