Multiple scale and singular perturbation methods
This book is a revised and updated version, including a substantial portion of new material, of the authors' widely acclaimed earlier text "Perturbation Methods in Applied Mathematics". A new chapter dealing with regular expansions has been added, the discussion of layer-type singular perturbations has been revised, and the coverage of multiple scale and averaging methods has been significantly expanded to reflect recent advances and viewpoints. The result is a comprehensive account of the vari…
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- Full title :Multiple scale and singular perturbation methods / J. Kevorkian, J.D. Cole.
Summary
This book is a revised and updated version, including a substantial portion of new material, of the authors' widely acclaimed earlier text "Perturbation Methods in Applied Mathematics". A new chapter dealing with regular expansions has been added, the discussion of layer-type singular perturbations has been revised, and the coverage of multiple scale and averaging methods has been significantly expanded to reflect recent advances and viewpoints. The result is a comprehensive account of the various perturbation techniques currently used in the sciences and engineering, and is suitable for a graduate text as well as a reference work on the subject.
Read More ↓Edition Statements
- Publication Date:1996
Publication Statements
- Publisher(s):Springer-Verlag New York
- Place of Publication:New York, NY
- Language:eng
- Publication Date:1996
The Physical Object
- Description:1 online resource (viii, 648 pages) : : illustrations
Edition Identifiers
- ISBN:9781461239680, 1461239680, 0387942025, 9780387942025
- DOI:10.1007/978-1-4612-3968-0
- oclc:ocn852790561
- LC Classification:QA371
- Dewey Decimal:515.35
Table of Contents
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 F…
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