Approximation Procedures in Nonlinear Oscillation Theory (De Gruyter Series in Nonlinear Analysis & Applications): 2 3110141329, 9783110141320
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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
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