Introduction to Singular Perturbations

Introduction to Singular Perturbations

1st Edition - January 28, 1974

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  • Author: Robert E. Jr. O'Malley
  • eBook ISBN: 9780323162272

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Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.

Table of Contents

  • Preface

    Chapter 1. First Concerns

    1. Examples of Singular Perturbation Problems

    2. Asymptotic Expansions

    3. Intuitive Approach of Matched Asymptotic Expansions

    4. Two-Variable Expansions

    Chapter 2. The Regular Perturbation Method

    Chapter 3. Linear Boundary Value Problems

    1. Second-Order Problems

    2. Higher-Order Problems

    3. Generalizations of These Results

    Chapter 4. Nonlinear Initial Value Problems

    1. The Basic Problem

    2. Two-Parameter Problems

    3. Differential-Difference Equations with Small Delay

    Chapter 5. Nonlinear Boundary Value Problems

    1. Some Second-Order Scalar Problems

    2. Second-Order Quasi-Linear Equations

    3. Quasi-Linear Systems

    4. An Extended Discussion of a Nonlinear Example

    Chapter 6. The Singularly Perturbed Linear State Regulator Problem

    Chapter 7. Boundary Value Problems with Multiple Solutions Arising in Chemical Reactor Theory

    Chapter 8. Some Turning Point Problems

    1. A Simple Problem

    2. A Uniform Reduction Theorem

    3. The Boundary Value Problem



Product details

  • No. of pages: 214
  • Language: English
  • Copyright: © Academic Press 1974
  • Published: January 28, 1974
  • Imprint: Academic Press
  • eBook ISBN: 9780323162272

About the Author

Robert E. Jr. O'Malley

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