Robert E. O'Malley

Singular Perturbation Methods for Ordinary Differential Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

The book is intended to be used as a textbook and a reference to learn about singular perturbation methods and their use in applications. The presentation is closely related to current mathematics and applied literature and is written to be accessible to students of mathematics, engineering, and the sciences.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 227
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461209775
• Artikelnr.: 43986967

Inhaltsangabe

1: Examples Illustrating Regular and Singular Perturbation Concepts.- A. The Harmonic Oscillator: Low Frequency Situation.- B. Introductory Definitions and Remarks.- C. A Simple First-Order Linear Initial Value Problem.- D. Some Second-Order Two-Point Problems.- E. Regular Perturbation Theory for Initial Value Problems.- 2: Singularly Perturbed Initial Value Problems.- A. A Nonlinear Problem from Enzyme Kinetics.- B. The Solution of Linear Systems Using Transformation Methods.- C. Inner and Outer Solutions of Model Problems.- D. The Nonlinear Vector Problem (Tikhonov-Levinson Theory).- E. An Outline of a Proof of Asymptotic Correctness.- F. Numerical Methods for Stiff Equations.- G. Relaxation Oscillations.- H. A Combustion Model.- I. Linear and Nonlinear Examples of Conditionally Stable Systems.- J. Singular Problems.- 3: Singularly Perturbed Boundary Value Problems.- A. Second Order Linear Equations (without Turning Points).- B. Linear Scalar Equations of Higher Order.- C. First-Order Linear Systems.- D. An Application in Control Theory.- E. Some Linear Turning Point Problems.- F. Quasilinear Second-Order Problems.- G. Existence, Uniqueness, and Numerical Computation of Solutions.- H. Quasilinear Vector Problems.- I. An Example with an Angular Solution.- J. Nonlinear Systems.- K. A Nonlinear Control Problem.- L. Semiconductor Modeling.- M. Shocks and Transition Layers.- N. Phase-Plane Solutions for Conservative Systems.- O. A Geometric Analysis for Some Autonomous Equations.- P. Semilinear Problems.- Appendix: The Historical Development of Singular Perturbations.- References.