Multiple scale and singular perturbation methods

✍ Scribed by J Kevorkian; Julian D Cole

• Publisher: Springer
• Year: 1996
• Tongue: English
• Leaves: 642
• Series: Applied mathematical sciences (Springer-Verlag New York Inc.), v. 114
• Category: Library

✦ Table of Contents

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Preface......Page 6
Contents......Page 8
1.1. Order Symbols, Uniformity......Page 10
1.2. Asymptotic Expansion of a Given Function......Page 14
1.3. Regular Expansions for Ordinary and Partial Differential Equations......Page 28
References......Page 44
2.1. The Linear Oscillator......Page 45
2.2. Linear Singular Perturbation Problems with Variable Coefficients......Page 62
2.3. Model Nonlinear Example for Singular Perturbations......Page 91
2.4. Singular Boundary Problems......Page 104
2.5. Higher-Order Example: Beam String......Page 119
References......Page 126
3.1. Limit Process Expansions for Second-Order Partial Differential Equations......Page 127
3.2. Boundary-Layer Theory in Viscous, Incompressible Flow......Page 173
3.3. Singular Boundary Problems......Page 191
References......Page 273
4. The Method of Multiple Scales for Ordinary Differential Equations......Page 276
4.1. Method of Strained Coordinates for Periodic Solutions......Page 277
4.2: Two Scale Expansions for the Weakly Nonlinear Autonomous Oscillator......Page 289
4.3. Multiple-Scale Expansions for General Weakly Nonlinear Oscillators......Page 316
4.4. Two-Scale Expansions for Strictly Nonlinear Oscillators......Page 368
4.5. Multiple-Scale Expansions for Systems of First-Order Equations in Standard Form......Page 395
References......Page 417
5. Near-Identity Averaging Transformations: Transient and Sustained Resonance......Page 419
5.1. General Systems in Standard Form: Nonresonant Solutions......Page 420
5.2. Hamiltonian System in Standard Form; Nonresonant Solutions......Page 449
5.3. Order Reduction and Global Adiabatic Invariants for Solutions in Resonance......Page 491
5.4. Prescribed Frequency Variations, Transient Resonance......Page 511
5.5. Frequencies that Depend on the Actions, Transient or Sustained Resonance......Page 522
References......Page 529
6.1. Nearly Periodic Waves......Page 531
6.2. Weakly Nonlinear Conservation Laws......Page 560
6.3. Multiple-Scale Homogenization......Page 623
References......Page 628
Index......Page 630