The theory of singular perturbations /

The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of sol...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Jager, E. M. de (Eduardus Marie de)
Otros Autores: Furu, Jiang
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; New York : Elsevier, 1996.
Colección:North-Holland series in applied mathematics and mechanics ; v. 42.
Temas:
Singular perturbations (Mathematics)
Perturbations singuli�eres (Math�ematiques)
MATHEMATICS > Differential Equations > General.
Differentiaalvergelijkingen.
Storingsrekening.
Singulariteiten.
Acceso en línea:Texto completo
Texto completo
Tabla de Contenidos:
  • Cover
  • Contents
  • Preface
  • Chapter 1. General Introduction
  • Chapter 2. Asymptotic Expansions
  • 1 Order Symbols
  • 2 Gauge Functions and Asymptotic Sequences
  • Asymptotic Series
  • 4 Convergence versus Asymptotic Convergence
  • 5 Elementary Operations on Asymptotic Expansions
  • 6 Other Types of Estimates
  • 7 Generalized Asymptotic Expansions
  • Exercises
  • Chapter 3. Regular Perturbations
  • 1 Regular Perturbations
  • 2 A Nonlinear Initial Value Problem Containing a Small Parameter
  • 3 Applications
  • Chapter 4. The Method of the Strained Coordinate
  • 1 Introduction
  • 2 Applications of the Method of the Strained Coordinate
  • 3 The Method of the Strained Parameter
  • 4 Lighthill's Method
  • 5 Temple's Method
  • 6 Limitations of the Lindstedt-Poincar�e Method
  • Exercises
  • Chapter 5. The Method of Averaging
  • 1 Introduction
  • 2 The Krilov-Bogoliubov-Mitropolski Theorem
  • 3 Weakly Nonlinear Free Oscillations
  • 4 Weakly Forced Nonlinear Oscillations
  • 5 A Linear Oscillator with Increasing Damping
  • Exercises
  • Chapter 6. The Method of Multiple Scales
  • 1 Introduction
  • 2 Weakly Nonlinear Free Oscillations
  • 3 The Linear Oscillator with Damping
  • 4 The Equation of Mathieu
  • 5 The General Case and the Error Estimate
  • 6 Averaging and Multiple Scales for Perturbed Wave Equations
  • Exercises
  • Chapter 7. Singular Perturbations of Linear Ordinary Differential Equations
  • 1 The initial Value Problem
  • 2 The Boundary Value Problem
  • 3 Boundary Value Problems with Turning Points
  • Exercises
  • Chapter 8. Singular Perturbations of Second Order Elliptic Type. Linear Theory
  • 1 Introduction
  • 2 The Maximum Principle for Elliptic Operators
  • 3 The Formal Approximation
  • 4 Estimation of the Remainder Term and Final Results
  • 5 Domains with Characteristic Boundaries
  • 6 Elliptic Boundary Value Problems with Turning Points
  • Exercises
  • Chapter 9. Singular Perturbations of Second Order Hyperbolic Type.
  • 1 Introduction
  • 2 Characteristics and Subcharacteristics
  • 3 The Formal Approximation
  • 4 A Priori Estimates of Solutions of Initial Value Problems for Partial Differential Equations with a Singular Perturbation of Hyperbolic Type
  • 5 The Estimate of the Remainder Term and Final Results
  • Exercises
  • Chapter 10. Singular Perturbations in Nonlinear Initial Value Problems of Second Order
  • 1 Introduction
  • 2 A Fixed Point Theorem
  • 3 The Quasilinear Initial Value Problem
  • 4 A General Nonlinear Initial Value Problem
  • 5 Quasilinear Initial Value Problems with a Singular Perturbation of Second Order Hyperbolic Type
  • Exercises
  • Chapter 11. Singular Perturbations in Nonlinear Boundary Value Problems of Second Order
  • 1 Introduction
  • 2 Boundary Value Problems for Quasilinear Ordinary Differential Equations
  • 3 Transition Layers
  • 4 Autonomous Conservative Equations
  • 5 A More General Case
  • 6 Boundary Value Problems for Quasilinear Partial Differential Equations of Elliptic Type
  • Exercises
  • Chapter 12. Perturbations of Higher Order
  • 1 Introduction
  • 2 Perturbations of Higher Order in Ordinary Differential Equations
  • 3 Elliptic Perturbations of Elliptic Equations
  • 4 Elliptic Singular Perturbations of Higher Order
  • Exercises.

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