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Approximation procedures in nonlinear oscillation theory /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bobylev, N. A.
Otros Autores: Burman, Yu. M. (Yuri M.), 1967-, Korovin, S. K., 1945-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin ; New York : W. de Gruyer, 1994.
Colección:De Gruyter series in nonlinear analysis and applications ; 2.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface
  • Contents
  • Chapter I: Basic Concepts
  • Â 1 Equations for oscillatory systems
  • Â 2 The shift operator and first return function
  • Â 3 Integral and integrofunctional operators for periodic problem
  • Â 4 The harmonic balance method
  • Â 5 The method of mechanical quadratures
  • Â 6 The collocation method
  • Â 7 The method of finite differences
  • Â 8 Factor methods
  • Chapter II: Existence theorems for oscillatory regimes
  • Â 1 Smooth manifolds and differential forms
  • Â 2 Degree of a mapping
  • Â 3 Rotation of vector fields
  •  4 Completely continuous vector fields 5 Fixed point principles and solution of operator equations
  • Â 6 Forced oscillations in systems with weak nonlinearities
  • Â 7 Oscillations in systems with strong nonlinearities. Directing functions method
  • Chapter III: Convergence of numerical procedures
  • Â 1 Projection methods
  • Â 2 Factor methods
  • Â 3 Convergence of the harmonic balance method and the collocation method in the problem of periodic oscillations
  • Â 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
  • Â 7 Affinity theory
  • Â 8 Effective convergence criteria for numerical procedures
  • Â 9 Effective estimates of the convergence rate for the harmonic balance method
  • Notes on the References
  • References
  • Index