Author | O'Malley, Robert E. author |
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Title | Singular Perturbation Methods for Ordinary Differential Equations [electronic resource] / by Robert E. O'Malley |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0977-5 |
Descript | VIII, 227 p. online resource |
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 (TikhonovโLevinson 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