Author | Kevorkian, J. author |
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Title | Multiple Scale and Singular Perturbation Methods [electronic resource] / by J. Kevorkian, J. D. Cole |
Imprint | New York, NY : Springer New York, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3968-0 |
Descript | VIII, 634 p. online resource |
1. Introduction -- 1.1. Order Symbols, Uniformity -- 1.2. Asymptotic Expansion of a Given Function -- 1.3. Regular Expansions for Ordinary and Partial Differential Equations -- References -- 2. Limit Process Expansions for Ordinary Differential Equations -- 2.1. The Linear Oscillator -- 2.2. Linear Singular Perturbation Problems with Variable Coefficients -- 2.3. Model Nonlinear Example for Singular Perturbations -- 2.4. Singular Boundary Problems -- 2.5. Higher-Order Example: Beam String -- References -- 3. Limit Process Expansions for Partial Differential Equations -- 3.1. Limit Process Expansions for Second-Order Partial Differential Equations -- 3.2. Boundary-Layer Theory in Viscous, Incompressible Flow -- 3.3. Singular Boundary Problems -- References -- 4. The Method of Multiple Scales for Ordinary Differential Equations -- 4.1. Method of Strained Coordinates for Periodic Solutions -- 4.2. Two Scale Expansions for the Weakly Nonlinear Autonomous Oscillator -- 4.3. Multiple-Scale Expansions for General Weakly Nonlinear Oscillators -- 4.4. Two-Scale Expansions for Strictly Nonlinear Oscillators -- 4.5. Multiple-Scale Expansions for Systems of First-Order Equations in Standard Form -- References -- 5. Near-Identity Averaging Transformations: Transient and Sustained Resonance -- 5.1. General Systems in Standard Form: Nonresonant Solutions -- 5.2. Hamiltonian System in Standard Form; Nonresonant Solutions -- 5.3. Order Reduction and Global Adiabatic Invariants for Solutions in Resonance -- 5.4. Prescribed Frequency Variations, Transient Resonance -- 5.5. Frequencies that Depend on the Actions, Transient or Sustained Resonance -- References -- 6. Multiple-Scale Expansions for Partial Differential Equations -- 6.1. Nearly Periodic Waves -- 6.2. Weakly Nonlinear Conservation Laws -- 6.3. Multiple-Scale Homogenization -- References